Phy Review Question Motion

Question

A mass M is suspended from a spring and oscillates with a period of 0.960 s. Each complete oscillation results in an amplitude reduction of a factor of 0.965 due to a small velocity dependent frictional effect. Calculate the time it takes for the total energy of the oscillator to decrease to 59% of its initial value.

Answer 1

Note that e^-.96/τ=.965. Solve to find τ (time constant) = 26.95 sec. Now set e-t/26.95=.59. Solve for t = 14.22 sec