How Do You Calculate Maximum Speed in Spring Oscillations?

[K3nt70]

[SOLVED] More Spring oscillation

Homework Statement

A 2.20 kg mass is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 17.6 N is required to hold the mass at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The mass is now released from rest with an initial displacement of xi = 0.200 m, and it subsequently undergoes simple harmonic oscillations. Calculate the maximum speed of the mass.

I've calculated the following already:
Spring constant is 88.0 N/m
Oscillation frequency is 1.00 Hz

Homework Equations

This is pretty much the problem; i don't know what equation to use to get the max velocity

The Attempt at a Solution

Ive been messing around with V = -AwSin(wt) but i can't fathom how to get amplitude..

 

[Hootenanny]

HINT: The amplitude is given in the question.

 

[K3nt70]

mkay, well the only thing i can see close to amplitude is Xi. But if that's amplitude, then all i have left to find is time..

 

[Hootenanny]

mkay, well the only thing i can see close to amplitude is Xi. But if that's amplitude, then all i have left to find is time..

x_i is indeed the amplitude. However, there is no need to consider the amplitude, period, angular velocity etc. This problem can be trivially solved using conservation of energy.

 

[K3nt70]

Ek = 1/2 mv^2, but i don't have kenetic energy...

 

[Hootenanny]

Ek = 1/2 mv^2, but i don't have kenetic energy...

No you don't have the kinetic energy, but you can work out the initial potential energy...

 

[K3nt70]

Ep= 1/2 kX^2 <-- is this the equation you're referring to?

 

[Hootenanny]

Ep= 1/2 kX^2 <-- is this the equation you're referring to?

Indeed it is, and since energy is conserved you can use this to determine the velocity of the mass at any point.

 

[K3nt70]

woohoo! Thanks for your help!

 

[Hootenanny]

woohoo! Thanks for your help!

No problem

Don't forget to mark the thread as 'solved' when your done.