Hum Ass Due In a five supe grou orga The subm The for suffi conc and The and off’ w The angr they Que Wha Man man Res signmen e Date: N Marketing employee ervisor has up membe anization. task given mitted to t forecasts special in cient to ke cerned wit he is inclin members seemingly work. employee ry that the y speak to h estion: at are th nagement source M nt No. 01 Novemb g Departm es, who wo s his office ers are we to the gro the market are mostl formation eep all five th the spe ned to leav of group a y unimport es would li eir supervi him. he proble deal with t Manage 1 ber 26, 2 ent of an ork closely e two floo ell‐educate oup is to p ting manag ly routine, is receiv e group m cial respon ve the grou are frustra tant – alth ike to initi sor does n ems in a this situat ment (M 2015 organizati y together ors above ed, but m repare ma ger whose , although ved. The v embers bu nsibilities up alone. ated becau hough they iate more not show above sce ion? MGT501) ion, the w r in an op in the sa most of th arket forec office is in occasiona volume of usy. The gr which kee use much y sometim of their o any intere enario an ) F M ork group pen‐plan o ame buildi hem are n casts, whic n a differe ally ‘one‐o f work is roup’s lead ep him ful of the wo mes enjoy d own projec est in this nd how Fall 2015 Marks: 1 consists o office. The ing. All th new to th ch would b nt building off’ reques not reall der is mor ly occupie rk is borin doing ‘one cts and ar idea whe might th 5 0 of ir e e be g. st ly re d ng ere n e DEAD   FORM     REFE  RULE     DLINE: Make sure Any subm MATTING GU Use the fo It is advise You may a Use black ERENCING G Use APA Google an http://lin ES FOR MAR Please not It is subm The file yo It is in any It is cheat e to upload th mission made UIDELINES: ont style “Tim ed to compo also compos and blue fon GuIDELINES style for refe nd read vario guistics.byu.e RKING: te that your a mitted after th ou uploaded y format othe ed or copied he solution f via email aft mes New Ro ose your docu e your assign nt colors only : erencing and ous website c edu/faculty/ assignment w he due date. does not op er than MS-W d from other file before the ter the due d oman” or “Ar ument in MS nment in Op y. citation. Fo containing in /henrichsenl/ will not be co en or is corru Word or Ope students, int e due date on ate will not b rial” and fon S-Word form en Office fo or guidance s nformation fo /apa/APA01 onsidered, if: upt. en Office; e.g ternet, books n VULMS. be accepted. nt size “12”. mat. rmat. search “APA or better und 1.html g. Excel, Pow s, journals etc A reference st derstanding o werPoint, PD c. tyle” in or visit DF etc.

Hum Ass Due In a five supe grou orga The subm The for suffi conc and The and off’ w The angr they Que Wha Man man Res signmen e Date: N Marketing employee ervisor has up membe anization. task given mitted to t forecasts special in cient to ke cerned wit he is inclin members seemingly work. employee ry that the y speak to h estion: at are th nagement source M nt No. 01 Novemb g Departm es, who wo s his office ers are we to the gro the market are mostl formation eep all five th the spe ned to leav of group a y unimport es would li eir supervi him. he proble deal with t Manage 1 ber 26, 2 ent of an ork closely e two floo ell‐educate oup is to p ting manag ly routine, is receiv e group m cial respon ve the grou are frustra tant – alth ike to initi sor does n ems in a this situat ment (M 2015 organizati y together ors above ed, but m repare ma ger whose , although ved. The v embers bu nsibilities up alone. ated becau hough they iate more not show above sce ion? MGT501) ion, the w r in an op in the sa most of th arket forec office is in occasiona volume of usy. The gr which kee use much y sometim of their o any intere enario an ) F M ork group pen‐plan o ame buildi hem are n casts, whic n a differe ally ‘one‐o f work is roup’s lead ep him ful of the wo mes enjoy d own projec est in this nd how Fall 2015 Marks: 1 consists o office. The ing. All th new to th ch would b nt building off’ reques not reall der is mor ly occupie rk is borin doing ‘one cts and ar idea whe might th 5 0 of ir e e be g. st ly re d ng ere n e DEAD   FORM     REFE  RULE     DLINE: Make sure Any subm MATTING GU Use the fo It is advise You may a Use black ERENCING G Use APA Google an http://lin ES FOR MAR Please not It is subm The file yo It is in any It is cheat e to upload th mission made UIDELINES: ont style “Tim ed to compo also compos and blue fon GuIDELINES style for refe nd read vario guistics.byu.e RKING: te that your a mitted after th ou uploaded y format othe ed or copied he solution f via email aft mes New Ro ose your docu e your assign nt colors only : erencing and ous website c edu/faculty/ assignment w he due date. does not op er than MS-W d from other file before the ter the due d oman” or “Ar ument in MS nment in Op y. citation. Fo containing in /henrichsenl/ will not be co en or is corru Word or Ope students, int e due date on ate will not b rial” and fon S-Word form en Office fo or guidance s nformation fo /apa/APA01 onsidered, if: upt. en Office; e.g ternet, books n VULMS. be accepted. nt size “12”. mat. rmat. search “APA or better und 1.html g. Excel, Pow s, journals etc A reference st derstanding o werPoint, PD c. tyle” in or visit DF etc.

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EEGR 221 MATLAB Project 1 Basic Signals Fall 2015 Due date: 10/5/15 1. (a) Plot ?1(?) = ?(?+1)−?(?−5) where -7 < t < 7 seconds. Use millisecond units. (b) Plot ? = 5 ??? (??)[ ?(?+1)−?(?−5)] 2. (a) Plot x2(t) exactly as shown in this figure. Include the same titles and labels for the signal. Hint: Find the amplitude equations as function of time and insert those to your MATLAB script to create and plot this signal. (b) Decompose x2(t) into its even and odd components and plot x2e(t) and x2o(t). (c) Plot x2e(t) + x2o(t) and verify that x2e(t) + x2o(t) = x2(t). How to report the results?  For each plot you must label x and y axis and have a title for the plot. Following commands could be used. heaviside, plot, axis, ylabel, ylabel, title, fliplr, etc … At the command prompt of MATLAB you can type >> help [command name] to get help with any command.  Plot all of the signal for t between -7 and 7 seconds.  Save your commands in an m-file with your name in the name field. (e.g. John_Scott.m) and append the code to the end of your report.  Your report must be organized and your solution for each question mu st be clearly marked by the number of the question. Example 2.a or 2.b, … In each part the problem should be clearly identified. Type the problem statement in each section. Show the plots of input and output signals. Draw conclusions based on your plots and in problem 3 discuss why the property is not satisfied based on your plots.  Turn in a hard copy of your report in class. This report must include a cover page with the name of both student partners.

EEGR 221 MATLAB Project 1 Basic Signals Fall 2015 Due date: 10/5/15 1. (a) Plot ?1(?) = ?(?+1)−?(?−5) where -7 < t < 7 seconds. Use millisecond units. (b) Plot ? = 5 ??? (??)[ ?(?+1)−?(?−5)] 2. (a) Plot x2(t) exactly as shown in this figure. Include the same titles and labels for the signal. Hint: Find the amplitude equations as function of time and insert those to your MATLAB script to create and plot this signal. (b) Decompose x2(t) into its even and odd components and plot x2e(t) and x2o(t). (c) Plot x2e(t) + x2o(t) and verify that x2e(t) + x2o(t) = x2(t). How to report the results?  For each plot you must label x and y axis and have a title for the plot. Following commands could be used. heaviside, plot, axis, ylabel, ylabel, title, fliplr, etc … At the command prompt of MATLAB you can type >> help [command name] to get help with any command.  Plot all of the signal for t between -7 and 7 seconds.  Save your commands in an m-file with your name in the name field. (e.g. John_Scott.m) and append the code to the end of your report.  Your report must be organized and your solution for each question mu st be clearly marked by the number of the question. Example 2.a or 2.b, … In each part the problem should be clearly identified. Type the problem statement in each section. Show the plots of input and output signals. Draw conclusions based on your plots and in problem 3 discuss why the property is not satisfied based on your plots.  Turn in a hard copy of your report in class. This report must include a cover page with the name of both student partners.

Lab 5 Math 551 Fall 2015 Goal: In this assignment we will look at two fractals, namely the Sierpinski fractal and the Barnsley Fern. During the lab session, your lab instructor will teach you the necessary MATLAB code to complete the assignment, which will be discussed in the lab on Thursday October 8th or Friday October 9th in the lab (CW 144 or CW 145). What you have to submit: An m- le containing all of the commands necessary to perform all the tasks described below. Submit this le on Canvas. Click: \Assignments”, click \MATLAB Project 5″, click \Submit Assignment”, then upload your .m le and click \Submit Assignment” again. Due date: Friday October 16, 5pm. No late submission will be accepted. TASKS A fractal can be de ned as a self-similar detailed pattern repeating itself. Some of the most well know fractals (the Mandelbrot set and Julia set) can be viewed here: http://classes.yale.edu/fractals/ The Sierpinski Fractal The program srnpnski(m,dist,n) gets its name from the mathematician W. Sierpinski. The only parameter that must be speci ed is m which determines the number of vertices that will be part of a regular polygon. For larger m it produces a graph which is similar to a snow ake. The program starts with a randomly chosen seed position given by the internal variable s. At each stage one of the vertices is chosen at random and a new point is produced which is dist away from the old point to the vertex. The value of dist should be between 0 and 1. The default value is 0.5. This process is repeated n times. The default value of n is 1500. 1. Create a new Matlab function: func t i on s rpns k i (m, di s t , n) %This c r e a t e s a snowf lake from m v e r t i c e s us ing n i t e r a t i o n s . i f nargin <3, n=1500; end i f nargin <2, d i s t =0.5; end c l f a x i s ( [ ?1 ,1 , ?1 ,1] ) p=exp (2 pi  i  ( 1 :m)/m) ; pl o t (p , '  ' ) hold s=rand+i  rand ; f o r j =1:n r=c e i l (m rand ) ; s=d i s t  s+(1?d i s t )p( r ) ; pl o t ( s , ' . ' ) end 2. Try out the following commands s rpns k i ( 3 ) s rpns k i ( 3 , 0 . 5 , 2 5 0 0 ) s rpns k i ( 3 , 0 . 5 , 5 0 0 0 ) s rpns k i ( 3 , 0 . 4 ) 1 s rpns k i ( 3 , 0 . 2 ) s rpns k i ( 5 ) s rpns k i ( 5 , 0 . 4 ) s rpns k i ( 5 , 0 . 3 ) s rpns k i ( 6 , 0 . 3 ) s rpns k i ( 8 , 0 . 3 , 5 0 0 0 ) The Barnsley Fern The following program is the famous Barnsley Fern. The only external parameter is n, the number of iterations. 3. Create a new Matlab function: func t i on f e r n (n) A1=[ 0 . 8 5 , 0 . 0 4 ; ?0 . 0 4 , 0 . 8 5 ] ; A2=[ ?0 . 1 5 , 0 . 2 8 ; 0 . 2 6 , 0 . 2 4 ] ; A3=[ 0 . 2 , ?0 . 2 6 ; 0 . 2 3 , 0 . 2 2 ] ; A4=[ 0 , 0 ; 0 , 0 . 1 6 ] ; T1=[ 0 ; 1 . 6 ] ; T2=[ 0 ; 0 . 4 4 ] ; T3=[ 0 ; 1 . 6 ] ; T4=[ 0 , 0 ] ; P1=0.85; P2=0.07; P3=0.07; P4=0.01; c l f ; s=rand ( 2 , 1 ) ; pl o t ( s ( 1 ) , s ( 2 ) , ' . ' ) hold f o r j =1:n r=rand ; i f r<=P1 , s=A1 s+T1 ; e l s e i f r<=P1+P2 , s=A2 s+T2 ; e l s e i f r<=P1+P2+P3 , s=A3 s+T3 ; e l s e s=A4 s ; end pl o t ( s ( 1 ) , s ( 2 ) , ' . ' ) end 4. Try the following commands: f e r n (100) f e r n (500) f e r n (1000) f e r n (3000) f e r n (5000) f e r n (10000) 2 5. Change the parameters in the fern program: A1=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; A2=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; A3=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; T1=[ 1 ; 1 ] ; T2=[ 1 ; 5 0 ] ; T3=[ 5 0 ; 5 0 ] ; P1=0.33; P2=0.33; P3=0.34; Call the new program srptri.m. Try the command s r p t r i (5000) You should see a familiar looking result. 6. Change the parameters in the fern program: A1=[ 0 , 0 ; 0 , 0 . 5 ] ; A2=[ 0 . 4 2 , ?0 . 4 2 ; 0 . 4 2 , 0 . 4 2 ] ; A3=[ 0 . 4 2 , 0 . 4 2 ; ?0 . 4 2 , 0 . 4 2 ] ; A4=[ 0 . 1 , 0 ; 0 , 0 . 1 ] ; T1=[ 0 ; 0 ] ; T2=[ 0 ; 0 . 2 ] ; T3=[ 0 ; 0 . 2 ] ; T4=[ 0 , 0 . 2 ] ; P1=0.05; P2=0.4; P3=0.4; P4=0.15; Call the new program srptree.m. Try the command s r p t r e e (5000) This is an example of a fractal tree. Some nice animations of fractal trees can be seen here: http://classes.yale.edu/fractals/ MATLAB commands to learn: Cl f , c e i l , imaginary uni t I , i f . . e l s e i f . . e l s e . . end 3

Lab 5 Math 551 Fall 2015 Goal: In this assignment we will look at two fractals, namely the Sierpinski fractal and the Barnsley Fern. During the lab session, your lab instructor will teach you the necessary MATLAB code to complete the assignment, which will be discussed in the lab on Thursday October 8th or Friday October 9th in the lab (CW 144 or CW 145). What you have to submit: An m- le containing all of the commands necessary to perform all the tasks described below. Submit this le on Canvas. Click: \Assignments”, click \MATLAB Project 5″, click \Submit Assignment”, then upload your .m le and click \Submit Assignment” again. Due date: Friday October 16, 5pm. No late submission will be accepted. TASKS A fractal can be de ned as a self-similar detailed pattern repeating itself. Some of the most well know fractals (the Mandelbrot set and Julia set) can be viewed here: http://classes.yale.edu/fractals/ The Sierpinski Fractal The program srnpnski(m,dist,n) gets its name from the mathematician W. Sierpinski. The only parameter that must be speci ed is m which determines the number of vertices that will be part of a regular polygon. For larger m it produces a graph which is similar to a snow ake. The program starts with a randomly chosen seed position given by the internal variable s. At each stage one of the vertices is chosen at random and a new point is produced which is dist away from the old point to the vertex. The value of dist should be between 0 and 1. The default value is 0.5. This process is repeated n times. The default value of n is 1500. 1. Create a new Matlab function: func t i on s rpns k i (m, di s t , n) %This c r e a t e s a snowf lake from m v e r t i c e s us ing n i t e r a t i o n s . i f nargin <3, n=1500; end i f nargin <2, d i s t =0.5; end c l f a x i s ( [ ?1 ,1 , ?1 ,1] ) p=exp (2 pi  i  ( 1 :m)/m) ; pl o t (p , '  ' ) hold s=rand+i  rand ; f o r j =1:n r=c e i l (m rand ) ; s=d i s t  s+(1?d i s t )p( r ) ; pl o t ( s , ' . ' ) end 2. Try out the following commands s rpns k i ( 3 ) s rpns k i ( 3 , 0 . 5 , 2 5 0 0 ) s rpns k i ( 3 , 0 . 5 , 5 0 0 0 ) s rpns k i ( 3 , 0 . 4 ) 1 s rpns k i ( 3 , 0 . 2 ) s rpns k i ( 5 ) s rpns k i ( 5 , 0 . 4 ) s rpns k i ( 5 , 0 . 3 ) s rpns k i ( 6 , 0 . 3 ) s rpns k i ( 8 , 0 . 3 , 5 0 0 0 ) The Barnsley Fern The following program is the famous Barnsley Fern. The only external parameter is n, the number of iterations. 3. Create a new Matlab function: func t i on f e r n (n) A1=[ 0 . 8 5 , 0 . 0 4 ; ?0 . 0 4 , 0 . 8 5 ] ; A2=[ ?0 . 1 5 , 0 . 2 8 ; 0 . 2 6 , 0 . 2 4 ] ; A3=[ 0 . 2 , ?0 . 2 6 ; 0 . 2 3 , 0 . 2 2 ] ; A4=[ 0 , 0 ; 0 , 0 . 1 6 ] ; T1=[ 0 ; 1 . 6 ] ; T2=[ 0 ; 0 . 4 4 ] ; T3=[ 0 ; 1 . 6 ] ; T4=[ 0 , 0 ] ; P1=0.85; P2=0.07; P3=0.07; P4=0.01; c l f ; s=rand ( 2 , 1 ) ; pl o t ( s ( 1 ) , s ( 2 ) , ' . ' ) hold f o r j =1:n r=rand ; i f r<=P1 , s=A1 s+T1 ; e l s e i f r<=P1+P2 , s=A2 s+T2 ; e l s e i f r<=P1+P2+P3 , s=A3 s+T3 ; e l s e s=A4 s ; end pl o t ( s ( 1 ) , s ( 2 ) , ' . ' ) end 4. Try the following commands: f e r n (100) f e r n (500) f e r n (1000) f e r n (3000) f e r n (5000) f e r n (10000) 2 5. Change the parameters in the fern program: A1=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; A2=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; A3=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; T1=[ 1 ; 1 ] ; T2=[ 1 ; 5 0 ] ; T3=[ 5 0 ; 5 0 ] ; P1=0.33; P2=0.33; P3=0.34; Call the new program srptri.m. Try the command s r p t r i (5000) You should see a familiar looking result. 6. Change the parameters in the fern program: A1=[ 0 , 0 ; 0 , 0 . 5 ] ; A2=[ 0 . 4 2 , ?0 . 4 2 ; 0 . 4 2 , 0 . 4 2 ] ; A3=[ 0 . 4 2 , 0 . 4 2 ; ?0 . 4 2 , 0 . 4 2 ] ; A4=[ 0 . 1 , 0 ; 0 , 0 . 1 ] ; T1=[ 0 ; 0 ] ; T2=[ 0 ; 0 . 2 ] ; T3=[ 0 ; 0 . 2 ] ; T4=[ 0 , 0 . 2 ] ; P1=0.05; P2=0.4; P3=0.4; P4=0.15; Call the new program srptree.m. Try the command s r p t r e e (5000) This is an example of a fractal tree. Some nice animations of fractal trees can be seen here: http://classes.yale.edu/fractals/ MATLAB commands to learn: Cl f , c e i l , imaginary uni t I , i f . . e l s e i f . . e l s e . . end 3

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Problems Marking scheme 1. Let A be a nonzero square matrix. Is it possible that a positive integer k exists such that ?? = 0 ? For example, find ?3 for the matrix [ 0 1 2 0 0 1 0 0 0 ] A square matrix A is nilpotent of index k when ? ≠ 0 , ?2 ≠ 0 , … . . , ??−1 ≠ 0, ??? ?? = 0. In this task you will explore nilpotent matrices. 1. The matrix in the example given above is nilpotent. What is its index? ( 2 marks ) 2. Use a software program to determine which of the following matrices are nilpotent and find their indices ( 12 marks ) A. [ 0 1 0 0 ] B. [ 0 1 1 0 ] C. [ 0 0 1 0 ] D. [ 1 0 1 0 ] E. [ 0 0 1 0 0 0 0 0 0 ] F. [ 0 0 0 1 0 0 1 1 0 ] 3. Find 3×3 nilpotent matrices of indices 2 and 3 ( 2 marks ) 4. Find 4×4 nilpotent matrices of indices 2, 3, and 4 ( 2 marks ) 5. Find nilpotent matrix of index 5 ( 2 marks ) 6. Are nilpotent matrices invertible? prove your answer ( 3 marks ) 7. When A is nilpotent, what can you say about ?? ? prove your answer ( 3 marks ) 8. Show that if ? is nilpotent , then ? − ? is invertible ( 4 marks ) 30% 2. A radio transmitter circuit contains a resisitance of 2.0 Ω, a variable inductor of 100 − ? ℎ?????? and a voltage source of 4.0 ? . find the current ? in the circuit as a function of the time t for 0 ≤ ? ≤ 100? if the intial curent is zero. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 3. An object falling under the influence of gravity has a variable accelertaion given by 32 − ? , where ? represents the velocity. If the object starts from rest, find an expression for the velocity in terms of the time. Also, find the limiting value of the velocity. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 4. When the angular displacement ? of a pendulum is small ( less than 60), the pendulum moves with simple harmonic motion closely approximated by ?′′ + ? ? ? = 0 . Here , ?′ = ?? ?? and ? is the accelertaion due to gravity , and ? is the length of the pendulum. Find ? as a function of time ( in s ) if ? = 9.8 ?/?2, ? = 1.0 ? ? = 0.1 and ?? ?? = 0 when ? = 0 . sketch the cuve using any graphical tool. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 5. Find the equation relating the charge and the time in a electric circuit with the following elements: ? = 0.200 ? , ? = 8.00 Ω , ? = 1.00 ?? , ? = 0. In this circuit , ? = 0 and ? = 0.500 ? when ? = 0 Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 6. A spring is stretched 1 m by ? 20 − ? Weight. The spring is stretched 0.5 m below the equilibrium position with the weight attached and the then released. If it is a medium that resists the motion with a force equal to 12?, where v is the velocity, sketch and find the displacement y of the weight as a function of the time. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 7. A 20?? inductor, a 40.0 Ω resistor, a 50.0 ?? capacitor, and voltage source of 100 ?−100?are connected in series in an electric circuit. Find the charge on the capacitor as a function of time t , if ? = 0 and ? = 0 ?ℎ?? ? = 0 Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 10% quality and neatness and using Math equations in MS word. –

Problems Marking scheme 1. Let A be a nonzero square matrix. Is it possible that a positive integer k exists such that ?? = 0 ? For example, find ?3 for the matrix [ 0 1 2 0 0 1 0 0 0 ] A square matrix A is nilpotent of index k when ? ≠ 0 , ?2 ≠ 0 , … . . , ??−1 ≠ 0, ??? ?? = 0. In this task you will explore nilpotent matrices. 1. The matrix in the example given above is nilpotent. What is its index? ( 2 marks ) 2. Use a software program to determine which of the following matrices are nilpotent and find their indices ( 12 marks ) A. [ 0 1 0 0 ] B. [ 0 1 1 0 ] C. [ 0 0 1 0 ] D. [ 1 0 1 0 ] E. [ 0 0 1 0 0 0 0 0 0 ] F. [ 0 0 0 1 0 0 1 1 0 ] 3. Find 3×3 nilpotent matrices of indices 2 and 3 ( 2 marks ) 4. Find 4×4 nilpotent matrices of indices 2, 3, and 4 ( 2 marks ) 5. Find nilpotent matrix of index 5 ( 2 marks ) 6. Are nilpotent matrices invertible? prove your answer ( 3 marks ) 7. When A is nilpotent, what can you say about ?? ? prove your answer ( 3 marks ) 8. Show that if ? is nilpotent , then ? − ? is invertible ( 4 marks ) 30% 2. A radio transmitter circuit contains a resisitance of 2.0 Ω, a variable inductor of 100 − ? ℎ?????? and a voltage source of 4.0 ? . find the current ? in the circuit as a function of the time t for 0 ≤ ? ≤ 100? if the intial curent is zero. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 3. An object falling under the influence of gravity has a variable accelertaion given by 32 − ? , where ? represents the velocity. If the object starts from rest, find an expression for the velocity in terms of the time. Also, find the limiting value of the velocity. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 4. When the angular displacement ? of a pendulum is small ( less than 60), the pendulum moves with simple harmonic motion closely approximated by ?′′ + ? ? ? = 0 . Here , ?′ = ?? ?? and ? is the accelertaion due to gravity , and ? is the length of the pendulum. Find ? as a function of time ( in s ) if ? = 9.8 ?/?2, ? = 1.0 ? ? = 0.1 and ?? ?? = 0 when ? = 0 . sketch the cuve using any graphical tool. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 5. Find the equation relating the charge and the time in a electric circuit with the following elements: ? = 0.200 ? , ? = 8.00 Ω , ? = 1.00 ?? , ? = 0. In this circuit , ? = 0 and ? = 0.500 ? when ? = 0 Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 6. A spring is stretched 1 m by ? 20 − ? Weight. The spring is stretched 0.5 m below the equilibrium position with the weight attached and the then released. If it is a medium that resists the motion with a force equal to 12?, where v is the velocity, sketch and find the displacement y of the weight as a function of the time. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 7. A 20?? inductor, a 40.0 Ω resistor, a 50.0 ?? capacitor, and voltage source of 100 ?−100?are connected in series in an electric circuit. Find the charge on the capacitor as a function of time t , if ? = 0 and ? = 0 ?ℎ?? ? = 0 Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 10% quality and neatness and using Math equations in MS word. –

Problems Marking scheme 1. Let A be a nonzero square … Read More...
1 REQUIREMENTS You will need to complete the following tasks and deliver your finding in a written report by August 6th. Research the six scenarios given below in option 1 for added capacity to uncover any additional costs/benefits to society these options might pose. Write a two page summary describing each scenario. Discuss the pros and cons of each scenario, including such items as renewable sources of fuel, environmental factors, etc. Give examples of each type of project by name and location and indicate the sources of your information. Please use either IEEE or APA style. Do an economic analysis of the six scenarios. Use a 20-year period and assume an inflation rate of 4 percent. Include your calculations and any assumptions in the report. Also answer the following questions: Which scenario is the best from an economic basis? Are there any other considerations, such as environmental/health/social issues, which should be considered? Which scenario have you selected based on the answers to a and b? What is the estimated timeframe to implement the different options? (base your timelines on existing projects of similar size if possible, use MS Project/Project Libre to generate the timelines) Make a recommendation regarding the best option for the utility. 2 Situations A utility company in one of the western states is considering the addition of 50 megawatts of generating capacity to meet expected demands for electrical energy by the year 2025. The three options that the utility has are: Add generating capacity. Constructing one of the scenarios below would do this. Purchase power from Canada under terms of a 20-year contract. Do neither of the above. This assumes that brownouts will occur during high demand periods. The utility presently has 200 megawatts of installed capacity and generates an average of 1.2 billion kilowatt-hours annually. Maximum generation capability is 1.3 billion kW-hours. By the year 2025, this reserve of 100,000,000 kW-hours will be used. 2.1 OPTION 1 – ADD GENERATING CAPACITY For this option there are six possible scenarios: Hydroelectric dam. Initial cost is $ 50 million. Annual operating and maintenance cost is $ 1.7 million. Project life is 30 years before a major rebuild is required. Wind farm. Initial cost is $ 28 million. Annual operating and maintenance cost is $ 2.5 million. Project life is 12 years. At this time new equipment will be required. Solar power. Initial cost is $ 32 million. Annual operating and maintenance cost is $ 1.1 million. Project life is 10 years. Natural gas turbines. Initial cost is $ 14 million. Annual operating and maintenance cost is $2.0 million. Project life is 12 years. Nuclear plant. Initial cost is $ 70 million. Annual operating and maintenance cost is $ 2.0 million. Project life is 25 years. Coal-fired turbines. Initial cost is $ 35 million. Annual operating and maintenance cost is $ 2.7 million. Project life is 28 years. 2.2 OPTION 2 – BUY POWER FROM CANADA The annual additional energy requirement is 350,000,000 kilowatt-hours. The cost of energy from Canada is 1.48 cents per kilowatt-hour for the first year. The price will be escalated at 4 percent annually for the 20-year contract period. 2.3 OPTION 3 – DO NOTHING Local municipalities are very opposed to this option since companies may have to close down for short periods of time. Also, it would be very difficult to attract new businesses. If nothing is done, by the year 2025 it is anticipated that some companies will be without power for short periods of time during the summer months. These are known as brownouts. It is estimated, based on historical data that these outages will occur once a week during July and August for periods of 6 hours.

1 REQUIREMENTS You will need to complete the following tasks and deliver your finding in a written report by August 6th. Research the six scenarios given below in option 1 for added capacity to uncover any additional costs/benefits to society these options might pose. Write a two page summary describing each scenario. Discuss the pros and cons of each scenario, including such items as renewable sources of fuel, environmental factors, etc. Give examples of each type of project by name and location and indicate the sources of your information. Please use either IEEE or APA style. Do an economic analysis of the six scenarios. Use a 20-year period and assume an inflation rate of 4 percent. Include your calculations and any assumptions in the report. Also answer the following questions: Which scenario is the best from an economic basis? Are there any other considerations, such as environmental/health/social issues, which should be considered? Which scenario have you selected based on the answers to a and b? What is the estimated timeframe to implement the different options? (base your timelines on existing projects of similar size if possible, use MS Project/Project Libre to generate the timelines) Make a recommendation regarding the best option for the utility. 2 Situations A utility company in one of the western states is considering the addition of 50 megawatts of generating capacity to meet expected demands for electrical energy by the year 2025. The three options that the utility has are: Add generating capacity. Constructing one of the scenarios below would do this. Purchase power from Canada under terms of a 20-year contract. Do neither of the above. This assumes that brownouts will occur during high demand periods. The utility presently has 200 megawatts of installed capacity and generates an average of 1.2 billion kilowatt-hours annually. Maximum generation capability is 1.3 billion kW-hours. By the year 2025, this reserve of 100,000,000 kW-hours will be used. 2.1 OPTION 1 – ADD GENERATING CAPACITY For this option there are six possible scenarios: Hydroelectric dam. Initial cost is $ 50 million. Annual operating and maintenance cost is $ 1.7 million. Project life is 30 years before a major rebuild is required. Wind farm. Initial cost is $ 28 million. Annual operating and maintenance cost is $ 2.5 million. Project life is 12 years. At this time new equipment will be required. Solar power. Initial cost is $ 32 million. Annual operating and maintenance cost is $ 1.1 million. Project life is 10 years. Natural gas turbines. Initial cost is $ 14 million. Annual operating and maintenance cost is $2.0 million. Project life is 12 years. Nuclear plant. Initial cost is $ 70 million. Annual operating and maintenance cost is $ 2.0 million. Project life is 25 years. Coal-fired turbines. Initial cost is $ 35 million. Annual operating and maintenance cost is $ 2.7 million. Project life is 28 years. 2.2 OPTION 2 – BUY POWER FROM CANADA The annual additional energy requirement is 350,000,000 kilowatt-hours. The cost of energy from Canada is 1.48 cents per kilowatt-hour for the first year. The price will be escalated at 4 percent annually for the 20-year contract period. 2.3 OPTION 3 – DO NOTHING Local municipalities are very opposed to this option since companies may have to close down for short periods of time. Also, it would be very difficult to attract new businesses. If nothing is done, by the year 2025 it is anticipated that some companies will be without power for short periods of time during the summer months. These are known as brownouts. It is estimated, based on historical data that these outages will occur once a week during July and August for periods of 6 hours.

1 REQUIREMENTS You will need to complete the following tasks … Read More...