Engineering Mechanics

Chapter 23 : Simple Harmonic Motion „„„„„ 479

We know that this resultant force of friction is equal to the product of mass of the bar and its
acceleration.

∴ Wx W aaor gx

ag a

μμ

=× =

Since the acceleration in the above equation is proportional to (i.e.*distance from the centre of
the bar), thus the bar executes a simple harmonic motion. Ans.

Periodic time

We know that periodic time in case of a simple harmonic motion,

Displacement

222

Acceleration

x

gx a

t

ag

μ

=π =π =π

μ

Ans.

EXERCISE 23.2

1. A particle moving with simple harmonic motion of amplitude 150 mm is subjected to an angular
   velocity of 2 rad/s. What is the maximum velocity and maximum acceleration of the particle?
   (Ans. 300 mm/s ; 600 mm/s^2 )


2. The time period of a simple harmonic motion is 6 seconds, and the particle oscillates through a
   distance of 300 mm on each side of the mean position. Find the maximum velocity and maximum
   acceleration of the particle. (Ans. 0.315 m/s ; 0.33 m/s^2 )

QUESTIONS

1. Explain the meaning of S.H.M. and give its one example.


2. Define the term amplitude as applied to S.H.M.


3. What do you understand by the terms ‘periodic time’ and ‘frequency’? What relation do they
   have?


4. Show that when a particle moves with simple harmonic motion, its time for a complete oscillation
   is independent of the amplitude of its motion.

OBJECTIVE TYPE QUESTIONS

1. The maximum displacement of a body moving with simple harmonic motion from its
   mean position is called
   (a) oscillation (b) amplitude (c) Beat (d ) none of them.


2. The frequency of vibration in case of simple harmonic motion
   (a) means the number of cycles per second
   (b) represents time taken by the particle for one complete oscillation
   (c) depends upon its amplitude.
   (d ) is directly proportional to its beat.

* For details, please refer to Art 23.3.