# Oscillator physics homework

1. Mar 23, 2008

### NAkid

1. The problem statement, all variables and given/known data
A mass M is suspended from a spring and oscillates with a period of 0.820s. Each complete oscillation results in an amplitude reduction of a factor of 0.985 due to a small velocity dependent frictional effect. Calculate the time it takes for the total energy of the oscillator to decrease to 0.500 of its initial value.

2. Relevant equations

3. The attempt at a solution

Tried .985^t = .5, then t = log(.5)/log(.985) but this didn't work... any other suggestions?

2. Mar 23, 2008

### Shooting Star

Try a direct and simple approach, without calculus. The total E of the spring is (1/2)kA^2, where A is the amplitude. For the energy to become E/2, you can find A.

After each oscillation, it becomes cA, where c = 0.985. If it starts out with amplitude A0 and energy E0, then you can calculate after how many swings the energy becomes E0, by using the above mentioned process. Then find the time.