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Chapter 11: Q39P (page 463)

(a) What is the period of small-angle oscillations of a simple pendulum with a mass of 0.1kgat the end of a string of length1m?(b) What is the period of small-angle oscillations of a meter stick suspended from one end, whose mass is0.1kg?

Short Answer

Expert verified

The period of small angle oscillations of a sample pendulum is 2.01 s.

The period of small angle oscillation of a meter stick suspended from one end is 1.64 s.

Step by step solution

01

Define oscillations of a simple pendulum.

A pendulum completes one oscillation when it begins at one extreme position A, goes to the opposite extreme point B, and then returns to A. The time period is the amount of time it takes to complete one oscillation. The oscillation's time period remains constant.

02

Find the period of small angle oscillations of a simple pendulum.

  1. The period of small angle oscillations of a sample pendulum is,

T=2蟺lg

Here, lis length of the pendulum and gis acceleration due to gravity.

Substitute 1mfor land 9.8m/s2for g.

T=2蟺1m9.8m/s2=2.01s

Therefore, the period of small angle oscillations of a simple pendulum is2.01s.

03

Find the period of small angle oscillation of a meter stick suspended from one end.

b. The period of small angle oscillation of a meter stick suspended from one end is,


T=2蟺Imgl'


Here,l'is length of stick from its center to the one end,mis mass of the scale and lis moment of inertia of the scale relative to one end.

The moment of inertia of the scale is,

I=13ml2


Substitute 13ml2for Iand l2for l'in equation T=2蟺Imgl'


T=2蟺13ml2mgl2=2蟺2l3g


Substitute 1mfor land 9.8m/s2for g.


T=2蟺21m39.8m/s2=1.64s

Therefore, the period of small angle oscillation of a meter stick suspended from one end is1.64s.

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