b Find the solution to mx cx kx f t x0 0 x0 0 for an ar

(b) Find the solution to
mx\'\' + cx\' + kx = f (t); x(0) = 0; x\'(0) = 0;
for an arbitrary function f (t), where m > 0, c > 0, k > 0, and c²-4km < 0 (system is underdamped).
Write the solution as a definite integral.

Solution

f*g is given by f(t)*g(t)

here f(t)=t and g(t)=sint

So we get,

f(t)*g(t)=t*sint

=tsint