PHSX 220 Homework 13 Paper – Due Online April 28 – 5:00 pm SHM and Wave the Equation Problem 1: A hanging mass system with a mass of 85 kg, spring constant of k= 490 N/m is realeased from rest from a distance of 10 meters below the systems equilibrium position (similar values to the bottom of a bungee jump). Calculate the following quantities in regards to this system after being released at t=0: a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system (Hz) c) The period of oscillations for the system (seconds) d) The time it takes to get back to the equilibrium position of the system for the rst time Problem 2: A horizontal spring-mass system (mass of 2:21×1025 kg) with no friction has an ocsillation frequency of 9,192,631,770 cycles per second. (a second is dened by 9,192,631,770 cycles of a Cs-133 atom)). Calculate the eective spring constant of the system Problem 3: A swinging person, such as Tarzan, can be modeled after a simple pendulum with a mass of 85 kg and a length of 10 m. Consider the mass being released from rest at t=0 at an angle of +15 degrees from the vertical. Calculate the following quantities in regards to this system. You need to be in radians mode for this problem a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system in (Hz) c) The period of oscillations of the system (seconds) d) Sketch plots of the angular position, angular velocity and angular acceleration of the system as a function of time. Hint: These will always help you with these time to it takes to a certain point in it’s cycle questions. e) The time it takes for the mass to get half way through its rst cycle (or to the other side of the swing if you were interested in timing say a rescue eort or something along those lines) . f) The maximum angular velocity of the mass g) The maximum angular accleration of the mass h) The magnitude of the angular momentum of the mass at 3 seconds i) The magnitude of the torque acting on the mass at 3 seconds Problem 4: A wave has a wavenumber of 1 m-1, and an angular frequency of 2 radians per second, travels in the +x direction and has a maximum transverse amplitude of 0.1 m. At t=0, and x =0 the y position is equal to 0.0 m (y(0,0) = 0.0 m). a) Calculate the wavelength of the wave b) Calculate the period of oscillations for the wave c) Calculate the wave speed along the x axis d) Calculate the magnitude and direction of the transverse position of the wave at x=0.5 m and t = 8s e) Calculate the magnitude and direction of the transverse velocity of the wave at x=0.5 m and t = 8s f) Calculate the magnitude and direction of the transverse acceleration of the wave at x=0.5 m and t = 8s Problem 5-6: Chapter 16 Problem 10, 22 Additional Suggested Problems with Solutions Provided: Chapter 16 Problems 5, 9, 15, 45

PHSX 220 Homework 13 Paper – Due Online April 28 – 5:00 pm SHM and Wave the Equation Problem 1: A hanging mass system with a mass of 85 kg, spring constant of k= 490 N/m is realeased from rest from a distance of 10 meters below the systems equilibrium position (similar values to the bottom of a bungee jump). Calculate the following quantities in regards to this system after being released at t=0: a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system (Hz) c) The period of oscillations for the system (seconds) d) The time it takes to get back to the equilibrium position of the system for the rst time Problem 2: A horizontal spring-mass system (mass of 2:21×1025 kg) with no friction has an ocsillation frequency of 9,192,631,770 cycles per second. (a second is dened by 9,192,631,770 cycles of a Cs-133 atom)). Calculate the eective spring constant of the system Problem 3: A swinging person, such as Tarzan, can be modeled after a simple pendulum with a mass of 85 kg and a length of 10 m. Consider the mass being released from rest at t=0 at an angle of +15 degrees from the vertical. Calculate the following quantities in regards to this system. You need to be in radians mode for this problem a) The angular frequency of the system (radians/sec) b) The frequency of oscillations for the system in (Hz) c) The period of oscillations of the system (seconds) d) Sketch plots of the angular position, angular velocity and angular acceleration of the system as a function of time. Hint: These will always help you with these time to it takes to a certain point in it’s cycle questions. e) The time it takes for the mass to get half way through its rst cycle (or to the other side of the swing if you were interested in timing say a rescue eort or something along those lines) . f) The maximum angular velocity of the mass g) The maximum angular accleration of the mass h) The magnitude of the angular momentum of the mass at 3 seconds i) The magnitude of the torque acting on the mass at 3 seconds Problem 4: A wave has a wavenumber of 1 m-1, and an angular frequency of 2 radians per second, travels in the +x direction and has a maximum transverse amplitude of 0.1 m. At t=0, and x =0 the y position is equal to 0.0 m (y(0,0) = 0.0 m). a) Calculate the wavelength of the wave b) Calculate the period of oscillations for the wave c) Calculate the wave speed along the x axis d) Calculate the magnitude and direction of the transverse position of the wave at x=0.5 m and t = 8s e) Calculate the magnitude and direction of the transverse velocity of the wave at x=0.5 m and t = 8s f) Calculate the magnitude and direction of the transverse acceleration of the wave at x=0.5 m and t = 8s Problem 5-6: Chapter 16 Problem 10, 22 Additional Suggested Problems with Solutions Provided: Chapter 16 Problems 5, 9, 15, 45

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