# Find the maximum acceleration and accleration of a mass spring system.

1. Dec 1, 2012

### Interception

1. The problem statement, all variables and given/known data
The problem states to find the maximum acceleration and velocity, the accleration and velocity when the displacement (x) is 1.00cm, and the equation of motion as a function of time if the displacement is A (amplitude) at t=0. We're given that the period (T) is 0.500s and the amplitude is 2.00cm with a total path length of 4.00 cm.

2. Relevant equations

Position as a function of time is given as x=cos(2$\pi$ft)
(v)max = 2$\pi$Af
A/(v) max = $\sqrt{m/k}$
k(spring constant) = m(2$\pi$f)^2

3. The attempt at a solution I found the frequency by take 1/0.50 to get 2 Hz. I then plugged into the (v) max equation to get 25.1 m/s. However, how do I find the spring constant and mass which I need to solve for acceleration? I really don't know how to approach this problem.

2. Dec 2, 2012

### haruspex

You shouldn't need to know the mass and spring constant separately. The quantities you need to calculate only depend on the ratio of the two. If you put in unknowns for them, they'll cancel out.