Two springs with negligible masses, one with spring constant k1 and the other with spring constant k2 are attached to the end stops of a level air track as in Figure P7.56. A glider attached to both springs is located between them. When the glider is in equilibrium, spring 1 is stretched by extension xil to the right of its unstretched length and spring 2 is stretched by xi2 to the left. Now a horizontal force F app is applied to the glider to move it a distance x2 to the right from its equilibrium position. Show that in this process
(a) The work done on spring 1 is ½ k1 (xa2 + 2xaxil),
(b) The work done on spring 2 is 1/2k2 (xa2 ─ 2xaxi2),
(c) Xi2 is related to xil by xi2 = k1xil/k2, and
(d) The total work done by the force Fapp is ½ (k1 + k2) xa2.