An object is suspended from the ceiling by a spring aligned along a vertical \(x\) axis, with upward defined as the positive \(x\) direction. When the spring is at its relaxed length, the object is at the origin of the axis. The object is pulled down to position \(-x_{1}\), held at rest, and released. Consider its motion from the instant of release until the instant it returns to \(-x_{1}\). Ignore friction, air drag, and the inertia of the spring.

(a) What force(s) is exerted on the object during the round trip, and in what direction(s)?

(b) How much work is done on the object by the spring as the object travels away from \(-x_{1}\) and back to \(-x_{1}\) ?