# Thread: Finding the equation of an oscillating mass

1. ## 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!

2. Use the equation $F=ke$ (Hooke's law) and $F=ma$.

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

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?

3. 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 $t = 0$, then the position in centimeters can be modeled by the equation

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

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