Question

An object is excuting simple harmonic motion. Which is a true statement regarding its motion?

a. its velocity is never zero

b. its acceleration is never zero

c. its velocity and accelertation are simultaneously zero

d. its velocity is zero when tis acceleration is a maximum

e. its acceleration is maximum when its velocity is maximum

Answer 1

Looking at the mathematic def. of symple harmonic motion

(1)

where A=amplitude, = angular frequency, t= time and =phase

we can get the function for velocity and acceleration:

(2)

(3)

an important result is that

In the figure below, there is a graph of the displacement, velocity and acceleration through 2 complete periods

the motion start at the origin when t=0. At this point, the velocity has its maximum magnitude and is positive, assuming that the body is moving to the right. The velocity does not change because the acceleration is zero.

After a quarter of a period , the body has moved to the right limit, and is about to return. The velocity is zero in this return point, but the acceleration has reached its maximum magnitude and it is negative, which means the body is moving to the left, and the velocity will be negative as well.

At this point we can eliminate options a, b,c and e. As we can see in the graph, acceleration and velocity can be zero but not simultaneously and, they cannot reach its maximum magnitude at the same time either.

Therefore, the correct answer is d, and it is clear to see in the figure where every quarter of a period the velocity is cero and the acceleration is maximum.