Amplitude of horizontal mass-spring system

[thatonenozz]

Homework Statement

This is a horizontal mass spring system in a simple harmonic motion problem set.

Vmax = 20 m/s
F = 10 N
m = 0.5 kg

Find Amplitude (A) and spring constant (k)

Homework Equations

The Attempt at a Solution

I could not figure out a way to solve this problem, and the only thing i could come up with was that the amplitude is equal to the x distance stretched. If this is true, then i can solve it using Hooke's law and other equations, but I'm not too sure it works out like that. Any help would be greatly appreciated!

 

[Steely Dan]

You are correct. Remember that the hallmark of simple harmonic motion is a sinusoidal time dependence for position, e.g.

$$x(t) = A\ \text{cos}(\omega t)$$

When $t = 0$, for instance, the position will be at its maximum value, which we call the amplitude of the motion.