# Analytic Problem

1. Oct 5, 2006

### jenkirk

Hey im new to this site, i used to have george jones as a proff he was an amazing guy but now this new proff i dont really get, i am having trouble with proofs, i dont know how to do them well i have 3 problems im having trouble with
given that the amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n cycles, show the ratio of period of oscillation to the period of the same oscillator with no damping is,
T (damped)/T(undamped) = square root (1+ 1/(4pi squared n squared)

The second question is: the terminal speed of a freely falling ball is v. when the ball is supported by a light elastic spring the spring stretches by an amount x, show the natural frewuency of oscillation is:
w (omega) = (square root g/x) - g/(2v)

haha hey im jen by the way

2. Oct 6, 2006

### Andrew Mason

What have you done? Can you write the expressions for $\omega$ for the damped oscillator ($m\ddot{x}+ b\dot{x} + kx = 0$) and $\omega_0$ for the undamped oscillator ($m\ddot{x} + kx = 0$).?

Can you determine the coefficients "b" and "k" in $m\ddot{x}+ b\dot{x} + kx = 0$?

AM

3. Oct 7, 2006

### jenkirk

im trying

hello, i have attempted the problem many times hahha, i know how to prove that w = square root (g/x) that is the easy part and the original question was w = square root of (g/x - (g squared /(4vsquared))) so i figured w squared then is equal to g/x - g squared /(4vsquared) trying to work backwards and i know that they start with
-kx + mg= 0 and k= mg/x so w= square root of mg/xm or g/x
im thinking its somewhere in this equation that i should be able to configure the right answer but i dont know
and for the first problem we have never done anythin with amplitude and period before so i just dont know where to put in 1/e?

p.s. how do you put in those symbols?

4. Oct 9, 2006

### George Jones

Staff Emeritus
What is the expression for the position of a particle undergoing damped harmonic motion?

What is the (time-dependent) amplitude of a damped harmonic oscllator?

It's LaTeX. You can look at examples by clicking on the mathematics in any post that uses it. Also, the tread Introducing https://www.physicsforums.com/showthread.php?t=8997" is very useful.

It takes a while to get the hang of LaTeX, and it can be a pain to use, but it does produce nice results.

Last edited by a moderator: Apr 22, 2017