   Chapter 13, Problem 72AP

Chapter
Section
Textbook Problem

An object of mass m is connected to two rubber bands of length L, each under tension F, as in Figure P13.72. The object is displaced vertically by a small distance y. Assuming the tension does not change, show that (a) the restoring force is −(2F/L)y and (b) the system exhibits simple harmonic motion with an angular frequency ω = 2 F / m L . Figure P13.72

a)

To determine
The restoring force exerted on the rubber band.

Explanation

Given info: The length of the two rubber bands are L . The rubber bands are under tension F . The mass of the object is m . The object is given a vertical displacement of y .

The system is shown in the following figure.

Consider the downward direction as negative. From the above figure, the restoring force on the rubber band is,

Fnet=2Fsinθ (1)

For small displacements

sinθ=tanθ (2)

Moreover the value of <

b)

To determine
The angular frequency of the simple harmonic motion.

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