How Long Until the Oscillator's Energy Halves?

[NAkid]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

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

 

[Shooting Star]

... any other suggestions?

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.