Prove that the particle is moving with simple harmonic motion

[itsmissnerdtoyo]

ok, so I've had a look around the forums and all that nd i can't find anything that will help me with what I am stuck on...nd if I'm about you ask a question that's already being asked I am sorry for posting a new thread...just point me in the right direction!

Homework Statement

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?

Homework Equations

so i know usually you compare it to the equation x=Acos(wt+phase) but i just don't 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!

 

[G01]

For the first part, your going to need to use a trig identity to get the function in terms of just one trig function. After this, it becomes obvious that it is a periodic function. You should then also be able to figure out ii) and iii) afterwards.

I'll leave it up to you to figure out what trig identity to use. Here is wikipedia's list:

http://en.wikipedia.org/wiki/Trigonometric_identity#Angle_sum_and_difference_identities

 

[sanjeeb]

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

 

[sanjeeb]

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

 

[itsmissnerdtoyo]

thanks so much! i got the answers, cheers*