   Chapter 13.3, Problem 13.4QQ

Chapter
Section
Textbook Problem

An object of mass m is attached to a horizontal spring, stretched to a displacement A from equilibrium, and released, undergoing harmonic oscillations on a frictionless surface with period T0. The experiment is then repeated with a mass of 4m. What’s the new period of oscillation? (a) 2T0 (b) T0 (c) T0/2 (d) T0/4

To determine
The period of the horizontal spring when a mass m is replaced by a mass 4m

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

T=2πmk

• T is the time period
• m is the mass of the object
• k is the force constant

Hence the time period is directly proportional to the square root of the mass of the object.

Conclusion:

Substitute 4m for m in the expression for T.

T=2π4mk=2(2πmk)

Substitute T0 for 2πmk in the above expression

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