Food and Beverages of Hotel, Recipe of Success.

CHAPTER 7

SIMPLE HARMONIC MOTION (SHM)

7.1 7.2 7.3 7.4

Simple Harmonic Motion (SHM) Kinematics of Simple Harmonic Motion Graph of Simple Harmonic Motion Period of Simple Harmonic Motion

7.1 Simple Harmonic Motion (SHM)

7.1 Simple Harmonic Motion (SHM)

Learning Outcome :
At the end of this topic, students should be able to:
 Explain SHM as a periodic motion without loss of energy  Describe SHM according to the formula :

d 2x a   2 x dt 2

7.1.1 SHM
 Simple harmonic motion (SHM) is a repeated motion of a particular frequency and period

 SHM also can be defined as a periodic motion without loss of energy and its acceleration is directly proportional to its displacement, x from a fixed point and always directed towards that fixed point

Vibrating Tuning fork

A weight on a spring

A boy on a swing

200 grams
Figure 1(a) Figure 1(b)

Figure 1(c)

Examples of SHM system
i. simple pendulum

 a  Fs m

Figure 2(a)

A ii. O

A

horizontal and vertical spring oscillations

A
O

 m  a Fs
A

A

m

  Fs a

A

O
Figure 2(c)

Figure 2(b)

Mathematically : d 2x   displacement, x acceleration, a  2

dt d 2x a   2 x dt 2

where

  angular velocity/angular frequency (positive
2

x

constant) displacement from the equilibrium position

* The angular frequency,  always constant, thus :

a x
* Negative sign denotes that the direction of the acceleration, a is in the opposite direction to the displacement x

The force causing the motion is in direct relationship to the displacement of the body (Hooke’s Law)

Elongation of spring \ F O R C E (N) 200 grams
Figure 3(a)

400 grams 600 grams

Slope = spring constant

Figure 3(b)

ELONGATION (M)

Figure 3(c)



SHM can also be defined as the motion of a body subjected to a resultant force which is directly proportional to its displacement from a fixed point and always directed towards