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Mechanical Properties of Fluids
Question
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A ball is dropped on a rigid floor and bounces back elastically. Will the ball execute simple harmonic motion?

Answer

No, the ball will not execute simple harmonic motion. 
It is not necessary that the ball should move to and fro around it's mean position. So, it will not undergo simple harmonic motion. 

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Some More Questions From Mechanical Properties of Fluids Chapter

Is there any relation between uniform circular motion and simple harmonic motion?

What is periodic motion?

Write down the expression for the instantaneous velocity and acceleration of particle vibrating in simple harmonic motion.

How do you define the mean position of particle executing simple harmonic motion?

Define amplitude.

What is the net displacement of the particle executing simple harmonic motion in one complete oscillation?

Are all the periodic motions simple harmonic?

Does the time period of particle vibrating in simple harmonic motion depend upon its displacement?

Where will the particle executing simple harmonic motion have acceleration maximum and speed zero?