Question

At what point(s) during the oscillation of a spring that obey's Hooke's law is the force on the mass the greatest?

Answer 1

only extreme poins obeys hooke's law if the force on the mass is greatest.

F = -k x

where F is the restoring elastic force exerted by the spring , k is the spring constant (N·m⁻¹), and x is the displacement from the equilibrium position (in m).

For any simple harmonic oscillator:

When the system is displaced from its equilibrium position, a restoring force which resembles Hooke's law tends to restore the system to equilibrium.

Once the mass is displaced from its equilibrium position, it experiences a net restoring force. As a result, it accelerates and starts going back to the equilibrium position. When the mass moves closer to the equilibrium position, the restoring force decreases. At the equilibrium position, the net restoring force vanishes. However, at x = 0, the mass has momentum because of the impulse that the restoring force has imparted. Therefore, the mass continues past the equilibrium position, compressing the spring. A net restoring force then tends to slow it down, until its velocity reaches zero, whereby it will attempt to reach equilibrium position again.

As long as the system has no energy loss, the mass will continue to oscillate. Thus, simple harmonic motion is a type of periodic motion.