# Mechanical vibrations

• Jan 27th 2009, 08:28 PM
s7b
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
• Jan 28th 2009, 04:57 AM
skeeter
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.