The figure shows a graph of the velocity v as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a function of time? a)

b)

c)

d)

A) graph a
B) graph b
C) graph c
D) graph d

Question

The figure shows a graph of the velocity v as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a function of time?

a)

b)

c)

d)

b)

c)

d)

A) graph a 
B) graph b 
C) graph c 
D) graph d

Quizplus · Accepted Answer

Acceleration is the derivative of velocity with respect to time. From the graph of velocity vs time, we can see that the maximum acceleration occurs at the points where the velocity is maximum (at the equilibrium position), and the acceleration is zero when velocity is zero (at the extreme positions). This means that the graph of acceleration vs time will be a cosine wave shifted 90 degrees ahead of the velocity vs time graph. The only graph that matches this description is graph B.

The Figure Shows a Graph of the Velocity V as a Function