The top graph represents the variation of displacement with time for a particle executing simple harmonic motion.Which curve in the bottom graph represents the variation of acceleration with time for the same particle?
A)1
B)2
C)3
D)4
E)None of these is correct.

Question

The top graph represents the variation of displacement with time for a particle executing simple harmonic motion.Which curve in the bottom graph represents the variation of acceleration with time for the same particle? 
A)1 
B)2 
C)3 
D)4 
E)None of these is correct.

Quizplus · Accepted Answer

The acceleration of a particle executing SHM is given by a = -ω^2x, where ω is the angular frequency and x is the displacement. Thus, the acceleration is proportional to the displacement but in the opposite direction. The curve in the bottom graph that represents this behavior is curve 2, which has a similar sinusoidal shape to the displacement curve but with opposite sign.

The Top Graph Represents the Variation of Displacement with Time