# Oscillations: Damped Block

1. Jun 16, 2011

### ThirdEyeBlind

1. The problem statement, all variables and given/known data
The drawing to the left shows a mass m= 1.8 kg hanging from a spring with spring constant k = 7 N/m. The mass is also attached to a paddle which is emersed in a tank of water with a total depth of 27 cm. When the mass oscillates, the paddle acts as a damping force given by -b(dx/dt) where b= 270 g/sec. Suppose the mass is pulled down a distance 1.1 cm and released.

a) What is the time required for the amplitude of the resulting oscillations to fall to one third of its initial value?
ΔT = 14.64816 sec

b) How many oscillations are made by the block in this time?
????????
2. Relevant equations

$$A(t)=A(0)e^{-bt/2m}$$
???

3. The attempt at a solution
I solved part a) and the computer verified my answer so I know its correct. I am just stuck on part b. I think I need to somehow find the period and then take the time in a) and divide it by the period. My book is confusing and I am not sure which equation to use.

EDIT: Finally found equation for period. It was T= 2pi sqrt (k/m) and then I took my answer from a) and divided it by the period to get the answer.

Last edited: Jun 16, 2011