Deriving time peroid of a spring

[thomas49th]

Hi all, I was wondering if we could go through how we get the time peroid for a spring with a mass m attached to it. The time period is:

T = 2pi sqrt(m/k)We know that F = -kx
We know the the the acceleration of a spring is always towards the equilibrium point
the speed can be measured negative and positive from the equilibrium point, as well as the displacement

The spring will be traveling fastest as it goes through the equilibrium point and it's displacement will be 0 at this point

Does that help towards the derivation?

Thanks
Tom

 

[rock.freak667]

F=ma

and the definition for simple harmonic motion will help

 

[HallsofIvy]

Hi all, I was wondering if we could go through how we get the time peroid for a spring with a mass m attached to it. The time period is:

T = 2pi sqrt(m/k)


We know that F = -kx
We know the the the acceleration of a spring is always towards the equilibrium point
the speed can be measured negative and positive from the equilibrium point, as well as the displacement

The spring will be traveling fastest as it goes through the equilibrium point and it's displacement will be 0 at this point

Does that help towards the derivation?

Thanks
Tom

F= ma= mx"= -kx.
Show that, for all numbers A and B,
$$x(t)= Acos(\sqrt{k/m}t)+ B sin(\sqrt{k/m}t)$$
satisfies that equation. What are the periods of those functions?