Question

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. Assume x=0 at t=0.

Thanks,
-nik

Answer 1

At t = 0, it is at the equilirium position t=0 but instantly acquires a velocity J/m. That is the maximum velocity during remaining oscillations.

The angular frequency of oscillation is w = sqrt (k/m),

V(t) = (J/m) cos wt


X(t) = integral of V(t)
= (1/w)(J/m) sin wt
= sqrt(mJ/k) sin wt