A particle of mass \(m\) is free to move in one dimension between the coordinates \(x=0\) and \(x=2 \pi / k\), where \(k\) is a positive constant. Within this range the particle is subject to the force \(F=\alpha \sin (k x)\), where \(\alpha\) is a constant.

(a) If the maximum value of the corresponding potential energy is \(\alpha / k\), what are the turning points of the particle if its energy is \(E=\alpha / 2 k\) ?

(b) Find the speed of the particle as a function of \(x\).