Please show work. Thank you. A 0.59 kg mass on a frictionless horizontal surface

Question

Please show work. Thank you.

A 0.59 kg mass on a frictionless horizontal surface is attached to a horizontal spring and vibrates 4.0 times per second with an amplitude of 0.15 m. Which is the correct equation describing the motion of the mass, assuming that x was a maximum at t = 0? x(t) = (0.15m) sin[2 pi(4.0 Hz)t] x(t) = (0.15m) cos[(4.0 Hz)t] x(t) = (0.15m) cos[2 pi(4.0 Hz)t] x(t) = (0.075m) cos[2 pi(4.0 Hz)t] Determine the total energy of the system. Express your answer using two significant figures.

Explanation / Answer

a) option c) x(t) = 0.15*cos[2*pi*(4 Hz)*t] because x will be max for t=0 for cos function.

b) The frequency of oscillation is:
= sqrt(k/m)
k/m = ^2
k = m*^2 = 0.59*(2**4)^2 = 372.7 N/m

At 0.15 m spring compression (amplitude), the energy is all Potential Energy (PE) in the spring:

PE = (1/2)*k*x^2 = (1/2)*372.7*(0.15^2) = 4.19 J

The maximum PE as calculated above is the total energy of the system. At the amplitude extremes it is all PE in the spring.

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