Question

When you pull a small tree to one side and suddenly let it go, it swings back and forth several times. You notice that the period of this motion doesn't depend on how far you bend the tree away from its normal upright position. Based on that observation, you know that the restoring force that returns the tree to its upright position is:_______.

Answer 1

Step-by-step explanation:

The period of oscillation of a SHM does not depend upon the amplitude of oscillation . But the restoring force depends upon the displacement . When the displacement is equal to amplitude , restoring force is the highest . this is the reason why in SHM , acceleration or deceleration depends upon the displacement from the point of equilibrium . Though time period remains the same.

Time period depends upon the elasticity of the material which creates restoring force and the mass of the body on which the restoring force acts.

Hence in the present case

the restoring force that returns the tree to its upright position is proportional to displacement from its equilibrium position.