# Spring and Hammer

1. Oct 3, 2004

### e(ho0n3

Problem: A mass m is at rest on the end of a spring of spring constant k. At t = 0 it is given an impulse J by a hammer. Write the formula for the subsequent motion in terms of m, k, J, and t.

Would ma = -kx + J/t be an acceptable answer?

2. Oct 3, 2004

### arildno

No, it is not!
The force associated by impulse J should be modeled by Dirac's delta function; solve the problem with Laplace Transforms.

Last edited: Oct 3, 2004
3. Oct 3, 2004

### e(ho0n3

Please note that the problem is from a general physics textbook. Assume as many simplifying assumptions as possible.

4. Oct 3, 2004

### arildno

In that case, solve it as follows:
Just after the impulse J, the mass has an initial velocity $$v_{0}=\frac{J}{m}$$
In the subsequent problem, your diffferential equation is:
$$-kx=m\ddot{x}$$
whereas initial conditions are:
$$x(0)=0,\dot{x}(0)=\frac{J}{m}$$

Last edited: Oct 3, 2004
5. Oct 3, 2004

### e(ho0n3

Hmm...Why didn't I think of that? I guess that does it for that problem. Thanks.