1. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA1
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

2. Simple Harmonic Motion S.H.M.
Sajjad Ahmed Memon
Senior Scientist
NIMRA

3. Simple Harmonic Motion
It is a type of periodic motion where the restoring force is directly proportional to the displacement. It can serve as a mathematical model of a variety of motions, such as the oscillation of a spring, motion of a simple pendulum etc.
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

4. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

5. Mass attached with Spring
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

6. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
Back and forth motion that is caused by a force that is directly proportional to the displacement. The displacement centers around an equilibrium position. Which is called Hooke’s Law
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

7. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
Where k is the spring constant and x is the displacement of the spring from its unstrained length. The minus sign indicates that the restoring force always points in a direction opposite to the displacement of the spring.
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

8. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
From Newton’s second law of motion Compare Newton’s second law of motion and Hooke’s Law simultaneously
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

9. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
The unit of “a” is meter/sec2 The unit of “m” is kg “x’” is measured in meters The unit of “k” is N/meter or kg/sec2 Where N=kg-meter/sec2
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

10. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

11. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
Also acceleration of a body in circular motion is given by Therefore
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

12. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
Since a cycle is 2p radians, the relationship between frequency and angular velocity is:
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

13. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
Therefore “f” is measured in sec-1 or Hz As “T” is in sec
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

14. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
Simple Pendulum
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

15. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

16. Forces acting on Bob/Ball
1. Weight of the bob (W) acting vertically downward. 2. Tension in the string (T) acting along the string. The weight of the bob can be resolved into two rectangular components: a. Wcosθ along the string. b. Wsinθ perpendicular to string.
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

17. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
Since there is no motion along the string, therefore, the component Wcosθ must balance tension (T) i.e. Wcosθ = T This shows that only Wsinθ is the net force which is responsible for the acceleration in the bob of pendulum. According to Newton's second law of motion Wsinθ will be equal to ma
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

18. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
i.e. Wsin θ = ma
Since Wsinθ is towards the mean position, therefore, it must have a negative sign. i.e. ma = - Wsinθ
But W = mg
ma = - mgsinθ
a = - gsinθ
In our assumption θ is very small because displacement is small, in this condition we can take sinθ = θ
Hence a = - gθ
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

19. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
If x be the linear displacement of the bob from its mean position, then from figure, the length of arc is nearly equal to x
From elementary geometry we know that:
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

20. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
The unit of “a” is meter/sec2 The unit of “l” is meter “x’” is measured in meters The unit of “g” is meter/sec2
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

21. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
Also acceleration of a body in circular motion is given by Therefore
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

22. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
Since a cycle is 2p radians, the relationship between frequency and angular velocity is:
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA

23. Sajjad Ahmed Memon S.S./ Health Physicist NIMRA
Therefore “f” is measured in sec-1 or Hz As “T” is in sec
Sajjad Ahmed Memon S.S./ Health Physicist NIMRA