Physics: Simple Harmonic Motion
posted by Greg on .
A 10kg particle undergoes simple harmonic motion with an amplitude of 2.0mm, a maximum acceleration of 8.0x10^3 m/s^2, and an unknown phase constant (phi) What are:
a.) the period of the motion
b.) the maximum speed of the particle
c.) total mechanical energy of the oscillator
What is the magnitude of the force on the particle when the particle is at:
d.) its maximum displacement
e.) half its maximum displacement
I have the answers from the back of the book, but I don't know which equations to use! Any help would be very appreciated!

I am going to assume you are in calculus.
x(t)=2E4 * sin(wt+Phi)
v(t)=w*2E4 * cos(wt+Phi)
a(t)=w^2*2E4 sin(wt+Phi)
You know the w=2PI/period, so given max a, find w, and then period.
then max speed.
total ME? 1/2 m (maxv)^2
for the last q, remember F=ma
You know max acceleration occures when the sin term is 1, so max a= w^2*2E4 
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