(a) Derive a general expression for the response of a uniform beam subjected to an arbitrary force.

(b) Use the result of part (a) to find the response of a uniform simply supported beam under the harmonic force \(F_{0} \sin \omega t\) applied at \(x=a\). Assume the initial conditions as \(w(x, 0)=(\partial w / \partial t)(x, 0)=0\).