   Chapter 13.4, Problem 13.6QQ

Chapter
Section
Textbook Problem

If the amplitude of a system moving in simple harmonic motion is doubled, which of the following quantities doesn’t change? (a) total energy (b) maximum speed (c) maximum acceleration (d) period

To determine
To determine which of the quantity does not change when the amplitude is doubled.

Explanation

Given info: The amplitude of the simple harmonic motion is doubled.

Explanation:

Amplitude ±A of a simple harmonic motion is the maximum displacement of the object from the equilibrium position.

The period for an object in simple harmonic motion is given by:

T=2πmk

Here,

T is the time period

m is the mass of the object

k is the force constant

The period of the simple harmonic motion is independent of the amplitude. Hence when the amplitude of the simple harmonic motion is doubled, there is no change in the period of the motion.

Conclusion:

The period of the motion T being independent of the amplitude of motion, does not change when the amplitude of the motion is doubled.

When the system under simple harmonic motion is in its turning positions, the total energy can be described in terms of the amplitude, A

E=12kA2

Here,

E is the total energy

k is the force constant

A is the amplitude of the simple harmonic motion

The total energy of the system in simple harmonic motion, directly proportional to the square of the amplitude. Hence when the amplitude is doubled, the total energy will become four time of the previous total energy. So option (a) is wrong.

When the system is in the turning points, the total energy is stored in the form of elastic potential energy

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