# Damped Harmonic Oscillator

## Homework Statement

A damped harmonic oscillator consists of a block (m = 2.72 kg), a spring (k = 10.3 N/m), and a damping force (F = -bv). Initially, it oscillates with an amplitude of 28.5 cm; because of the damping, the amplitude falls to 0.721 of the initial value at the completion of 7 oscillations. (a) What is the value of b? (Hint: Assume that b2 << km.) (b) How much energy has been lost during these 7 oscillations?

## The Attempt at a Solution

so first to find the period
T=2pi(m/k)^0.5
=2pi(2.72kg/10.3N/m)^0.5
=3.23 seconds
I know that this will be used in finding b, along with the mass, but I am clueless where to go from here. Part b was much easier to figure out with the energy lost being 0.2 J

I know the equation is (2m*ln(x))/(T*oscillations). Is the ln(x)=ln(1/%of energy retained)?

rude man
Homework Helper
Gold Member

## The Attempt at a Solution

so first to find the period
T=2pi(m/k)^0.5
That is not the period of the oscillations. (It would be if b=0).