- #1

seichan

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**[SOLVED] Dampened Harmonic Motion**

## Homework Statement

A mass M is suspended from a spring and oscillates with a period of 0.900 s. 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 50 percent of its initial value. HINT: The amplitude after N oscillations=(initial amplitude)x(factor)^N.

## Homework Equations

Newton's Second Law dampened- F=-kx-bv

x(t)=Ae^(-bt/2m)cos((dw/dt)t)

Energy=1/2kA^2 OR 1/2kv^2 [NOT constant]

## The Attempt at a Solution

Alright, I am having a difficult time setting this problem up. I do not know how to use the hint either... So far, I have set it up this way:

F=-kx-bv

The integral of this is equal to work. Negative work is equal to KE.

-1/2kx^2+1/2bv^2=1/2kv^2

I realized that this is as far as I can get with this, so I tried to use the x(t) equation. However, we are not given a value for the mass. I am very frustrated right now so any direction you can give would be very much appreciated.