A platform that rolls on wheels and has inertia \(m_{p}\) is attached to a wall by a horizontal spring of spring constant \(k\). A load of inertia \(m_{\ell}\) sits on the platform, and the coefficient of static friction between platform and load is \(\mu_{s}\). If you pull the platform away from the wall so that the spring is stretched a distance \(x\) from its relaxed length and then let go, the platform-spring combination bounces back and forth.

(a) At what position(s) in the motion is the load most likely to fall off?

(b) If you want the load to stay in place held only by friction, what is the maximum distance \(x_{\max }\) you can stretch the spring from its relaxed length and have the load stay on when you release the platform-spring combination?