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

The false statement is that a restoring force acts on an object in simple harmonic motion in the same direction as the object's displacement.

Step-by-step explanation:

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

In simple harmonic motion, the restoring force is proportional to the displacement and acts in the opposite direction of the displacement, as stated in statement B. Additionally, during simple harmonic motion, the net force on the object is indeed zero when it is at its equilibrium position, as stated in statement C. The displacement versus time graph for an object in simple harmonic motion resembles the sine or cosine function, as stated in statement D. Finally, the amplitude of the motion of an object in simple harmonic motion is indeed the maximum distance the object moves from its equilibrium position, as stated in statement E.

Answer 2

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

Step-by-step 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.