Deriving Simple Harmonic Motion Equations

[akj]

Hi i need help with this question. It is focused on simple harmonic equation and the rest of the assignment uses many question which are structure like this.

A mass of 16kg on a spring of k = 9.0N/m passes the midpoint of motion with a velocity of 2.0m/s what is the amplitutde?

I am unsure what equation(s) i could use that contains mass, spring contanstant (k), velocity and amplitute or displacement.

I would be greateful for any help,

thanks in advance.

 

[cscott]

You should really show us what you've tried.
Use the equation relating angular velocity, mass, and k.

Then take a look at the equation for velocity given by the conservation of energy.

Remember at the midpoint/equilibrium x = 0.

Oh, and post homework questions in the homework forum!

 

[akj]

thanks for your response. Are you referring to anqular velocity = square root[(k/m)]?. if so how do i relate this to working out the amplitute?

 

[mjsd]

instead of trying to dig out which equations to use, why not derive all of them yourself, that way u will understand everything a lot better.
start with key equation F=-kx = m x'' where x'' is the 2nd derivative. etc. then you will find a form for x in terms of sin/cos ..etc. then using basic relations like ang freq = 2 pi f, 1/f = period etc you can solve for everything. Amplitude will just be the factor outside your sin/cos functions. NB: you have been given some conditions so that you can fix some of your integration constants.