# Spring Problem

1. Dec 16, 2003

### etan

This was a problem on my final exam that I couldn't figure out, it drove me insane. Someone please tell me it's impossible

A spring has a 1kg block attached to it and a k of 30,000. A 2kg block moving at 30m/s over a frictionless surface hits and sticks to the 1kg block. What is the displacement of the spring? What frequency will it vibrate after impact?

I figured out that the final velocity of both blocks will be 20m/s and the final mass will be 3kg. I could not figure out the final acceleration to use m*a=x*k

I was not given the distance between the blocks or the time.

Any ideas?

2. Dec 16, 2003

### chroot

Staff Emeritus
Step 1) What is the kinetic energy of the resulting 3 kg lump?

Step 2) The work done by the lump in compressing the spring can be found by

$$W = \int F\, dx = \int kx\, dx = \frac{1}{2} kx^2$$

where W is equal to the kinetic energy of the lump.

The angular velocity of oscillation of a system with "springiness" k and mass m is

$$\omega = \sqrt{\frac{k}{m}$$

The frequency of an oscillation with angular velocity $\omega$ is

$$f = \frac{\omega}{2 \pi}$$

Does this make sense?

- Warren