Spring and Hammer

[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?

[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.

[e(ho0n3]

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

[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}

[e(ho0n3]

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