# Hey, so I am just working on a second year Analytical Mechanics

1. Oct 18, 2011

### Johnson

Hey, so I am just working on a second year Analytical Mechanics assignment, and right now dealing with oscillations. I have two questions I am stumped on and don't know if I have it right. It is probably basic, but just checking.

6. The frequency fd of a damped oscillator is 100 Hz, and the ratio of
the amplitudes of two successive maxima is one half. What is the
undamped frequency f0 of this oscillator?

e-$\gamma$Td = $\frac{1}{2}$
$\gamma$ = $\frac{1}{Td}$ln 2
fd ln 2
$\varpi$d = ($\varpi$02 - $\gamma$2)$\frac{1}{2}$
$\varpi$0 = ($\varpi$d2 + $\gamma$2)$\frac{1}{2}$
fo = [fd2 + $\frac{\gamma}{2\pi}$2]$\frac{1}{2}$
= fd[1+($\frac{ln2}{2\pi}$)2]$\frac{1}{2}$
fo = 100.6Hz

Is this correct?

7. An overdamped harmonic oscillator with ω0 = γ/2 is kicked out of equi-
librium x(t = 0) = 0 with the initial velocity v0. Find the displacement
x of the oscillator at time t = (2γ)-1.

As with this one, I don't know where to begin. Anyone be able to give me a hand starting it?

Cheers