# Damped harmonic oscillator

captainemeric

## Homework Statement

The displacement amplitude of a lightly damped oscillator with m=0.250kg and k=6400N/m is observed to decrease by 15% in exactly five minutes
a) Calculate the fraction (in%0 of the initial mechanical energy of the oscillator that has been converted to other forms of energy (such as thermal energy) in the five-minute interval.
b)Calculate the Q value of this damped oscillator by first calculation omega initial and gama

## Homework Equations

omega initial = sqrt(k/m)
gama = b/m
x = A initial exp^(gama t/2)
TE = 1/2kA initial exp^(-gamat)
A(t) = A inital exp^(bt/2m)
T = 2pisqrt(m/k)

## The Attempt at a Solution

I have calculated omega inital = 160rads and the period to be .04s. I know there is the relationship between the displacement amplitude and the total energy but I cannot seem to figure out how to relate them. Any help is greatly appreciated.

voko
At maximum displacement, what are the kinetic and potential energies of the oscillator?

captainemeric
At maximum displacement, the kinetic energy should be zero. Should I be able to solve for the potential energy? I am so confused as to how to approach this. I know I have been given enough info but I feel like I don't have enough to find any additional values.

voko
So at maximum displacement the entire energy is the potential energy. What is the potential energy of a spring?

captainemeric
1/2ka^2. How do i find this without being given a?

voko
What is a? What is amplitude?

captainemeric
Ok, so I finally figured out I can find the % of TE in relation to the % of A lost. Which I can also use to find b which I can then use to find Q.
A=Ainital exp^bt/2m where A/Ainital will equal .85 then the only unknown is b.
And TE goes as A^2 so if A is 85% then TE is .85^2 or ~72%