How Long Before an Oscillator's Energy Halves?

[fruitl00p]

Homework Statement

A mass M is suspended from a spring and oscillates with a period of .940s. Each complete oscillation results in an amplitude reduction of a factor of .96 due to a small velocity dependent of frictional effect. Calculate the time it takes for the total energy of the oscillator to decrease to .50 of its initial value.

Homework Equations

unsure... A=Ao*factor^N

The Attempt at a Solution

I am unsure how to approach this. I did

log .50 = t log(.96)^2
t= log(.50)/log(.96)^2
t=8.48 s

but that was incorrect. Can someone please tell me what I am doing wrong?

 

[AlephZero]

In you equation

log .50 = t log(.96)^2,

"t" isn't the time in seconds, it's the number of cycles of oscillation when the energy has decayed to .50 of the original value.

You want to time for 8.48 cycles with a period of 0.940 sec/cycle.

 

[fruitl00p]

Oh, I see now. I think I can handle the equation from here. Well, I'm going to attempt the problem again to make sure

 

[fruitl00p]

Yes, I got it correct, thank you AlephZero!