
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

for an ideal spring ...
Hooke's law (scalar version) ... $\displaystyle F = kx$
$\displaystyle F = mg$ = weight of the mass
$\displaystyle x$ = spring displacement
$\displaystyle k$ = spring constant
$\displaystyle mg = kx$
$\displaystyle k = \frac{mg}{x}$
amplitude of oscillation, $\displaystyle A$ = max displacement from equilibrium (was given to you).
angular frequency, $\displaystyle \omega = \sqrt{\frac{k}{m}}$
period of oscillation, $\displaystyle T = \frac{2\pi}{\omega}$
time from the bottom to the top would be half a period.
max speed, $\displaystyle v_{max} = A\omega$, occurs as the mass passes back and forth through equilibrium.