# Finding the equation of an oscillating mass

• Mar 27th 2009, 04:34 PM
uhhuh
Finding the equation of an oscillating mass
Hi, I really do not understand this question, if you could please solve and explain it, I would greatly appreciate it!

Here it is:

A mass on a spring oscillates back and forth. Its maximum displacement is 13.3 cm. Write an equation that models the motion.

Thanks you so much!
• Mar 28th 2009, 03:06 AM
Showcase_22
Use the equation $\displaystyle F=ke$ (Hooke's law) and $\displaystyle F=ma$.

ie. $\displaystyle ma=ke \Rightarrow \ m\frac{dv}{dt}=ke \Rightarrow \frac{dv}{dt}=\frac{ke}{m}$.

This is an expression for the rate of change of velocity, so you can use the chain rule to get an expression for the rate of change of displacement.

Can you take it from here?
• Mar 28th 2009, 06:38 AM
skeeter
Quote:

Originally Posted by uhhuh
Hi, I really do not understand this question, if you could please solve and explain it, I would greatly appreciate it!

Here it is:

A mass on a spring oscillates back and forth. Its maximum displacement is 13.3 cm. Write an equation that models the motion.

Thanks you so much!

note that you have some essential information that is missing, specifically, the period of oscillation.

if the mass starts at maximum displacement at time $\displaystyle t = 0$, then the position in centimeters can be modeled by the equation

$\displaystyle x = 13.3\cos(\omega t)$

where $\displaystyle \omega = \frac{2\pi}{T}$ , $\displaystyle T$ = period of the oscillation.