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Simple Harmonic Motion

Hi guys,

I have been doing some homework on SHM and I'm really not sure whether I'm doing this right. I would be grateful if I could just have some hints and tips here are there:

Firstly, a ball going back and forth along a horizontal floor bouncing off two vertical walls and a ball bouncing vertically off the floor are not examples of SHM...correct...?

I was then given information staing that a particle undergoing SHM has an amplitude of 8cm and frequency of 14Hz and when t=0, the displacement is 8cm. Therefore would the equation for displacement be:

8 cos 88t?

And is it normal to get numbers in the region of 10^4 for acceleration of this particle?

Finally:
I'm unsure about this question on a piston.
This piston has a "stroke" of 9cm and completes 4500 revs per minute?

I had to calculate the acceleration of the pisto at max displacement. Does a figure in the region fo 2x10^6 sound reasonable?

Also, would the velocity of the piston as it moves past its equilibrium point be 0 as the displacement would be 0?

Also, at max displacement, would the net force simply be calculated by using F=ma?

I'm sorry for the wealth of questions but I can't stand it when I don't fully understand what I'm working through.

Thanks!

Reply 1

Maniachris

First point is correct as the acceleration towards a position of equilibrium must be proportional to the objects displacement.

The equation for displacement is correct but it's best leave 88 as 2Pi14 for accuracy.

The acceleration A of the particle is given by the equation A = -(2Pif)^2 X
Where X is displacement from equilibrium postion. I got a value of 619 for the maximum acceleration.

For the acceleration of the piston frequency = 4500/60

A = (2Pi75)^2 x 9x10^-2
A = 2x10^5

When displacement is 0 the velocity will be at its maximum because the velocity/time graph is the gradient of a displacement graph. Basically the accelerating force towards the centre will of gone from its maximum to 0 as the object reaches equilibrium therefore its velocity will be at a maximum, then the accelerating force will act in the opposite direction again to decelerate the obeject and then accelerate it back towards equilibrium position.

At maximum displacement the net force = kx
(I think this is right) k=stiffness constant x=maximum displacement, that's if your given the stiffness constant, if your not then I guess the force would be equal to MA.

Reply 2

Graphix

Maniachris

First point is correct as the acceleration towards a posiition of equilibrium must be proportional to the objects displacement.

The equation for displacement is correct but it's best leave 88 as 2Pi14 for accuracy.

For the acceleration of the piston frequency = 4500/60

A = (2Pi75)^2 x 9x10^-2
A = 2x10^5

When displacement is 0 the velocity will be at its maximum because the velocity/time graph is the gradient of a displacement graph. Basically the accelerating force towards the centre will of gone from its maximum to 0 as the object reaches equilibrium therefore its velocity will be at a maximum, then the accelerating force will act in the opposite direction again to decelerate the obeject and then accelerate it back towards equilibrium position.

At maximum displacement the net force = kx
(I think this is right) k=stiffness constant x=maximum displacement, that's if your given the stiffness constant, if your not then I guess the force would be equal to MA.