PH4 SHM

Do you know the expression fot the period of oscillation of a mass-spring system in terms of the force constant and the mass? This question is basically assuming that the ions are oscillating in the same way, so you can work out T and hence f.

Reply 2

OP

Original post by Pangol

Do you know the expression fot the period of oscillation of a mass-spring system in terms of the force constant and the mass? This question is basically assuming that the ions are oscillating in the same way, so you can work out T and hence f.

I don't think I've heard of this constant before.
Is it something to do with this equation ?
T = 2(pi) root (l/g)

Reply 3

Force constant is another name for what you may know as the spring constant. It is the constant k in Hooke's Law, F = kx.

Reply 4

OP

Original post by Pangol

Force constant is another name for what you may know as the spring constant. It is the constant k in Hooke's Law, F = kx.

Yes I do know Hooke's law, but I don't see how to apply it here, in order to get T as you mentioned earlier ?
I'd assume k is 60 N/m and would the mass be the force ?

Reply 5

There's an equation that I think you sould know about mass-spring systems oscillating in SHM; T = 2 pi (m/k)^(1/2)

Reply 6

OP

Original post by Pangol

There's an equation that I think you sould know about mass-spring systems oscillating in SHM; T = 2 pi (m/k)^(1/2)

Awh right okay, I think I get it now, thank you!

Reply 7

OP

Original post by Pangol

There's an equation that I think you sould know about mass-spring systems oscillating in SHM; T = 2 pi (m/k)^(1/2)

Hi again, do you think you could help me on this question too please ? (:

A small mass on a platform P, vibrating vertically has an amplitude of 50mm.
At what frequency does the reaction of the platform become momentarily zero one point in the cycle, and where does this happen ?

I think it might have something to do with the weight and velocity equalling maybe ?

Reply 8

Start by thinking about the forces acting on the mass. There are only two, the weight acting down and the reaction force from the platform acting up. Assuming the mass is moving in SHM (which it is), you know and equation for the acceleration, and therefore the resultant force, that the mass experiences at any time. But this resultant force is made up of the two forces we were considering originally. So, you should have an equation along the lines of;

[acceleration, derived from resultant force, made up in some way of weight and reaction] = [some expression from an equation of SHM which includes amplitude and other stuff]

I know that's vague, but I'm trying not to give too much away! See of that gets you started.

Reply 9

OP

Original post by Pangol

Start by thinking about the forces acting on the mass. There are only two, the weight acting down and the reaction force from the platform acting up. Assuming the mass is moving in SHM (which it is), you know and equation for the acceleration, and therefore the resultant force, that the mass experiences at any time. But this resultant force is made up of the two forces we were considering originally. So, you should have an equation along the lines of;

[acceleration, derived from resultant force, made up in some way of weight and reaction] = [some expression from an equation of SHM which includes amplitude and other stuff]

I know that's vague, but I'm trying not to give too much away! See of that gets you started.

It's okay, thank you, I know I need to figure it out !

So F = ma result force is reaction - weight and using SHM a = -w

x^2

and the SHM ones I have are :
x = Asin (wt)
v = WA cos (wt)
a =

-w^2 A sin (wt)

Are they along the right lines ?

Reply 10