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Suppose you attach an object with mass to a vertical spring originally at rest, and let it bounce up and down. You release the object from rest at the spring's original rest length, the length of the spring in equilibrium, without the mass attached. The amplitude of the motion is the distance between the equilibrium position of the spring without the mase attached and the equilibrium position of the spring with the mass attached. (a) Show that the spring exerts an upward force of on the object at its lowest point. (b) If the spring has a force constant of , is hung horizontally, and the position of the free end of the spring is marked as , where is the new equilibrium position if a -mass object is hung from the spring? by during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?