Question

Q 10.17: Which of the following statements concerning simple harmonic motion is false? A : A restoring force acts on an object in simple harmonic motion that is directed in the same direction as the object's displacement. B : A restoring force acts on the object that is proportional to the object's displacement from its equilibrium position. C : During simple harmonic motion, the net force on the object is zero when it is at its equilibrium position. D : The displacement versus time graph for an object in simple harmonic motion resembles the sine or cosine function. E : The amplitude of the motion of an object in simple harmonic motion is the maximum distance the object moves from its equilibrium position.

Answer 1

Answer:

A : A restoring force acts on an object in simple harmonic motion that is directed in the same direction as the object's displacement.

Explanation:

Statement A is the false one:

A : A restoring force acts on an object in simple harmonic motion that is directed in the same direction as the object's displacement. --> FALSE. The restoring force in the simple harmonic motion is given by

$F=-kx$

where

k is the spring constant

x is the displacement of the system, measured with respect to the equilibrium position

As we can notice from the equation, there is a negative sign in front of (kx): this means that the force, F, and the displacement, x, have opposite directions. In fact, the restoring force of a simple harmonic oscillator always acts to restore the equilibrium position, therefore it acts in the opposite direction as that of the displacement.