A horizontal spring-mass system (mass of 2.21x 10^-25 kg) with no friction has a

Question

A horizontal spring-mass system (mass of 2.21x 10^-25 kg) with no friction has an oscillation frequency of 9,192,631,770 cycles per second. (a second is defined by 9,192,631,770 cycles of a Cs-133 atom)). Calculate the effective spring constant of the system 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 The angular frequency of the system (radians/sec) The frequency of oscillations for the system in (Hz) The period of oscillations of the system (seconds) Sketch plots of the angular position, angular velocity and angular acceleration of the system as a function of time. The time it takes for the mass to get half way through its first cycle (or to the other side of the swing if you were interested in timing say a rescue effort or something along those lines). The maximum angular velocity of the mass The maximum angular acceleration of the mass The magnitude of the angular momentum of the mass at 3 seconds The magnitude of the torque acting on the mass at 3 seconds

Explanation / Answer

1 / frequency = 2 * pi * sqrt(mass / spring constant)

1 / 9192631770 = 2 * pi * sqrt(2.21 * 10^-25 / spring constant)

spring constant = 0.000737279 N/m

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