# Simple Harmonic Motion

1. May 8, 2007

### newtonistheman

1. The problem statement, all variables and given/known data
A 10.0kg mass undergoes Simple Harmonic Motion with an amplitude of 8.0 cm, a maximum acceleration of magnitude 3.26 m/s^2, and an unknown phase constant φ. What is the period, max speed of the mass, the total mechanical energy of the system, and the magnitude of the force on the particle when it is at half of its maximum displacement?

2. Relevant equations
a=xm-w^2cos(wt+φ)

3. The attempt at a solution
3.26=8.0-w^2cos(wt+φ)
what do i use for the w?
How can we do this with out a phase.

2. May 8, 2007

### CaptainQuaser

Hints
phase doesn't matters, its just where you set 0 time. So you would start at some arbitrary location on the SHM curve.
Maximum velocity occurs at the eqbm position.
total energy is equivalent to kinetic energy at eqbm
maximum acceleration, instantaneous, occurs when v=0, aka all energy is potential at the peak of the SHM

and

try drawing the SHM curve, it helps to understand what is going on

Last edited: May 8, 2007
3. May 8, 2007

### CaptainQuaser

relevant equations
$\omega = 2 \pi f$
$T = \frac{1}{f}$