A \(50-\mathrm{kg}\) pneumatic hammer is fitted with a shock absorber at the top to lessen the impact on the worker. The vertical displacement of the hammer as a function of time is given by \(x(t)=a t^{2}-b t^{3}\) (during the hammer's bounce), where \(a=15 \mathrm{~m} / \mathrm{s}^{2}\) and \(b=20 \mathrm{~m} / \mathrm{s}^{3}\). The positive \(x\) axis is directed upward.

(a) Write an expression for the \(x\) component of the vector sum of forces exerted on the hammer as a function of time.

(b) At which values of \(t\) is the \(x\) component of the vector sum of forces on the hammer positive, at which values of \(t\) is it negative, and at which values of \(t\) is it zero?