Damped Harmonic Oscillation Question

• Apr 30th 2009, 08:21 PM
nosh
Damped Harmonic Oscillation Question

If a marble is placed on the end of a horizontal oscillating spring and the harmonic horizontal position of the marble as a function of time is given as :

If x = A ( 2 pi f t)

where A is amplitude
f is frequency

and t is time in seconds
If the spring oscillates every 0.5 seconds and has a maximum displacement of 0.2 m

what is the frequency?
what is the velocity as a function of time ?

how do you write the equation in the form given above for the position of the marble as a function of time ?
• May 1st 2009, 04:34 AM
Showcase_22
Isn't it $x=A \cos ( 2 \pi ft)$?

If the spring oscillates every 0.5 seconds, then isn't the frequency just $\frac{1}{0.5}=2$Hz?

The velocity is $v=\frac{dx}{dt}=-2 \pi Af \sin (2 \pi f t)$.

From here you can normally use the initial conditions to find A. When $t=0, v=0$.