Which one of the following statements about an object performing Simple Harmonic Motion is TRUE?

Select one:

a. The object reaches its maximum speed as it passes through the equilibrium point.

b. The object’s velocity is never zero.

c. The object has a constant velocity.

d. The object has a maximum magnitude of acceleration at the equilibrium point.

e. When the object’s velocity has its most negative value, then the acceleration has a maximum magnitude.

To determine which one of the statements is true, let's analyze each statement:

a. The object reaches its maximum speed as it passes through the equilibrium point.
This statement is incorrect. In simple harmonic motion, the object reaches its maximum speed at the equilibrium point, but not as it passes through it. At the equilibrium point, the object momentarily comes to rest before changing direction.

b. The object’s velocity is never zero.
This statement is also incorrect. In simple harmonic motion, the object's velocity is zero at both extreme points of its motion. At these points, the object reverses direction and changes from moving in one direction to moving in the opposite direction.

c. The object has a constant velocity.
This statement is false. In simple harmonic motion, the object does not have a constant velocity. Instead, its velocity changes constantly as it oscillates back and forth.

d. The object has a maximum magnitude of acceleration at the equilibrium point.
This statement is true. In simple harmonic motion, the object has a maximum magnitude of acceleration at the equilibrium point. The acceleration is maximum when the object is furthest from the equilibrium position.

e. When the object’s velocity has its most negative value, then the acceleration has a maximum magnitude.
This statement is false. In simple harmonic motion, the object's velocity is at its most negative value when it passes through the equilibrium position. However, the magnitude of acceleration is not maximum at this point. The magnitude of acceleration is maximum at the extreme points of the motion.

Based on the analysis, the true statement is:
d. The object has a maximum magnitude of acceleration at the equilibrium point.

The correct statement about an object performing Simple Harmonic Motion is:

d. The object has a maximum magnitude of acceleration at the equilibrium point.

x = a sin wt

v = a w cos wt
a = -a w^2 sin wt = -w^2 x

F = m a = -kx

when x = 0, equilibrium , sin wt = 0 and cos wt is 1. That is max velocity

when w t = pi/2, cos wt = 0 so v = 0

v = a w cos wt which is certainly not constant

a = -a w^2 sin wt = -w^2 x which is 0 when x = 0

v = a w cos wt max negative at t = 0
but then sin wt = 0 so acceleration is zero