# Prove that the particle is moving with simple harmonic motion

1. May 22, 2007

### itsmissnerdtoyo

ok, so i've had a look around the forums and all that nd i cant find anything that will help me with what im stuck on...nd if i'm about you ask a question thats already being asked im sorry for posting a new thread...just point me in the right direction!!!

1. The problem statement, all variables and given/known data
a particle is moving such that its displacement from equilibrium in metres is given by:
x = 5cos2t + 12sin2t

(i) prove that the particle is moving with simple harmonic motion
(ii) find the amplitude, angular frequency and period of the motion.
(iii) what is the velocity and acceleration of the particle as x = 12m?

2. Relevant equations

so i know usually you compare it to the equation x=Acos(wt+phase) but i just dont understand what to do in this case! and also....how do you prove the particle is moving with shm?! is it a=-w^2x???

cheers everyone*

oh nd sorry for just calling this post 'please help'....i should of perhaps called it something more specific! eep!

Last edited: May 22, 2007
2. May 22, 2007

### G01

3. May 22, 2007

### sanjeeb

hey differentiate x w.r.t t twice and find ur answer

4. May 22, 2007

### sanjeeb

for s.h.m, d2x/dt2 =-constant*x

5. May 23, 2007

### itsmissnerdtoyo

thanks so much! i got the answers, cheers*