Question

nalyzing the Motion of a Spring
An illustration of a mass on a vertical spring with a transverse wave showing the position of the mass on the spring will make a transverse wave shape if bouncing up and down and moving horizontally. The shortest spring has the mass at the top of each crest and are labeled A and E respectively. The position where the mass in in the trough of the transverse wave would be labeled C and stretches the spring the farthest. The middle length springs has masses where the equilibrium of the material of the medium containing the transverse wave would be at the equilibrium of the material would be and are labeled B and D.

At which point(s) is the net force the greatest?



At which point(s) is the net force zero?

Answer 1

Net force is largest where the mass is farthest from the static equilibrium (largest spring displacement), and it is zero where the mass is at the static equilibrium.

- Greatest net force: point C (the trough) — the spring is stretched the most so |x − x_eq| is largest, giving the largest restoring force.
(If the top crests A and E were equally far from equilibrium they would also have large net force, but the problem states C is the farthest.)

- Net force = 0: points B and D — these are the equilibrium positions where the spring force exactly balances the weight.