monkeyboy590
Sep29-09, 04:43 PM
1. The problem statement, all variables and given/known data
Given: The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n complete cycles. Show that the ratio of period of the oscillation to the period of the same oscillator with no damping is given by
T(sub d)/T(sub o) = (1 + (1/4(\pi^2)(n^2)))^1/2
2. Relevant equations
T(sub d) = (2\pi)/\omega_{d}
T(sub o) = (2\pi)/((k/m)^1/2)
A/A(sub o) = 1/2 = e^(-t/2\tau)
n = \omega_{d}t/2\pi
3. The attempt at a solution
I have tried dividing T(sub d) by T(sub o) to find a solution, and subbing known variables into the A/A(sub o) and n equations, to no avail. I have looked ahead to the solution to try to find a way to work towards it, but I don't know where I should start in order to go in the right direction.
Please help!
Given: The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n complete cycles. Show that the ratio of period of the oscillation to the period of the same oscillator with no damping is given by
T(sub d)/T(sub o) = (1 + (1/4(\pi^2)(n^2)))^1/2
2. Relevant equations
T(sub d) = (2\pi)/\omega_{d}
T(sub o) = (2\pi)/((k/m)^1/2)
A/A(sub o) = 1/2 = e^(-t/2\tau)
n = \omega_{d}t/2\pi
3. The attempt at a solution
I have tried dividing T(sub d) by T(sub o) to find a solution, and subbing known variables into the A/A(sub o) and n equations, to no avail. I have looked ahead to the solution to try to find a way to work towards it, but I don't know where I should start in order to go in the right direction.
Please help!