# Math Help - Mechanical vibrations

1. ## Mechanical vibrations

I was wondering if anyone would be able to start me off on this question;

A Weight stretches a spring 3 inches. It is set in motion at a point 4 inches below it's equilibrium position with zero velocity.
-Find the max amplitude
-Find the max velocity
-When does it reach it's highest point

2. for an ideal spring ...

Hooke's law (scalar version) ... $F = kx$

$F = mg$ = weight of the mass
$x$ = spring displacement
$k$ = spring constant

$mg = kx$

$k = \frac{mg}{x}$

amplitude of oscillation, $A$ = max displacement from equilibrium (was given to you).

angular frequency, $\omega = \sqrt{\frac{k}{m}}$

period of oscillation, $T = \frac{2\pi}{\omega}$

time from the bottom to the top would be half a period.

max speed, $v_{max} = A\omega$, occurs as the mass passes back and forth through equilibrium.