# Spring with Mass

1. Aug 3, 2006

### NotMrX

Suppose a spring with mass m and length L is connected to a rigid wall and a mass of M. Assuming no damping how do we find the frequency?

for the spring Density = m/L = D; dm = D dx
I don't know where to go from there.

2. Aug 3, 2006

### J Hann

The effective mass of a spring undergoing oscillatory motion is considered
to be 1/3 the mass of the spring. For any portion of the spring the
KE of dm is 1/2 dm * v^2. For a spring fixed at one end the velocity of an
element dm will be proportional to the distance from the fixed end - so
v = V*(y/Y) where Y is the length of the spring and V is the velocity of the moving end. Also, you can write dm = M * (dy/Y). Using these values
integrate 1/2 v^2 dm over the length of the spring to get the KE of the
oscillating spring and determine the effective mass of the spring.

3. Aug 5, 2006

### NotMrX

Thanks, I understand now.