- #1
superdave
- 150
- 3
Homework Statement
A damped harmonic oscillator has mass m , spring constant k , damping force
- cv .
(a) Find the ratio of two successive maxima of the oscillations.
(b) If the oscillator has Q = 100 , how many periods will it take for the amplitude to decay to 1/ e
of it’s initial value? What fraction of the initial energy the oscillator has left by this time?
Homework Equations
The Attempt at a Solution
Okay, so for a)
T_d=2pi/omega_d = 2pi/(omega_0^2 - gamma^2)
The ratio is equal to e^-(gamma * T_d)
so r = e^-(c/2m * 2pi/(k/m - (c/2m)^2)^1/2)
But then for b, I'm lost again.
If Q = 100, omega_d=200*gamma.
So the ratio of successive maxima = e ^ - pi/100
But I'm not sure how that let's me figure out how many periods will it take for the amplitude to decay to 1/ e of it’s initial value.