Question

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.

Answer 1

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