Quick SHM Question (1 Viewer)

[J-Wang]

"A particle is undergoing SHM on the x-axis about the origin. It is initially at its extreme positive position. The amplitude of the motion is 18 and the particle returns to its initial position every 5 seconds."

a. Write down an equation for the position of the particle at time t seconds.
b. How long does the particle take to move from a rest position to the point halfway between that rest position and the equilibrium position?

Can someone please explain to me how to approach this?

 

[J-Wang]

anyone know how?

 

[Carrotsticks]

A = 18 and since it returns to its position every 5 seconds, T = 5, where T is the period of motion.

So we can deduce that 2pi/n = 5 and hence n=2pi/5.

So the general equation of motion is x=18cos(2pi/5 t + alpha).

When t=0, x=18 since 'initially, it is at its extreme positive position'.

Sub that in to find alpha.

Then to do b), you need to sub x=9 (halfway) and then solve for t. This will give you the times it is at x=9.

Then sub x=18 and solve for t. This will give you the times it is at x=18 (endpoint).

Subtract the times.

Alternatively, you could integrate the velocity function from x=9 to x=18, once you have made T the subject and the integral is w.r.t. x