Question

A spring with spring constant 20.0N/m hangs from the ceiling. A 590g ball is attached to the spring and allowed to come to rest. It is then pulled down 7.10cm and released.
What is the time constant if the ball's amplitude has decreased to 2.40cm after 58.0 oscillations?

Answer 1

First calculate the period of oscillation.
P = 2*pi*sqrt(M/k) = 1.079 seconds
58.0 oscillations = 62.6 seconds

Amplitude = Ao*e(-t/T)
T is the time constant.
Use the 58 oscillation data point.
2.4/7.1 = 0.338 = e^(-62.6/T)
Solve for T
-1.085 = -62.6/T
T = 57.7 seconds

Answer 2

1=1