Simple harmonic motion And its application Presentation Slide

1. WELCOME TO MY
PRESENTATION

2. SIMPLE HARMONIC MOTION
AND ITS APPLICATION
PRESENTED BY
MD. SUMON SARDER
ID: 161-15-953

3. SIMPLE HARMONIC MOTION
BACK AND FORTH MOTION WHICH IS CAUSED BY A FORCE THAT IS
DIRECTLY PROPORTIONAL TO THE DISPLACEMENT. THE DISPLACEMENT
CENTERS AROUND AN EQUILIBRIUM POSITION.
xFs

4. Springs – Hooke’s Law
kxorkxF
k
k
xF
s
s



N/m):nitConstant(USpring
alityProportionofConstant

One of the simplest type of simple
harmonic motion is called Hooke's
Law. This is primarily in reference to
SPRINGS.

5. Simple Harmonic Motion (SHM)
Hence, In SHM the restoring force is proportional
to the displacement and acts in the opposite
direction of that displacement

6. Differential Equation of SHM

7. Value of 𝜔
Putting the solution in the differential equation we get the value of 𝜔
𝑑2
𝑥
𝑑𝑡2
+
𝑘
𝑚
𝑥 = 0
−𝜔2 𝐴𝑐𝑜𝑠 𝜔𝑡 + 𝜙 +
𝑘
𝑚
𝐴𝑐𝑜𝑠 𝜔𝑡 + 𝜙 = 0
𝜔 =
𝑘
𝑚

8. Time Period of SHM
If we increase the time t in the solution of SHM by
2𝜋/𝜔, the function becomes,
𝑥 = 𝐴𝑐𝑜𝑠 𝜔 𝑡 +
2𝜋
𝜔
+ 𝜙
= 𝐴𝑐𝑜𝑠 𝜔𝑡 + 2𝜋 + 𝜙
= 𝐴𝑐𝑜𝑠 𝜔𝑡 + 𝜙
i.e. the function repeats itself after a time 2𝜋/𝜔
Therefore 2𝜋/𝜔 is the period of the motion, T.
𝑇 =
2𝜋
𝜔
𝜔 =
2𝜋
𝑇
= 2𝜋𝑓, is the angular frequency.

9. Velocity & Acceleration

11. Total Energy in SHM

12. Applications of SHM
As per Hooke’s law the restoring force on a spring is F=-kx,
the exact condition for simple harmonic oscillation.

13. Simple Pendulum

14. The Torsional Oscillator

15. The Physical Pendulum
If we locate the pivot far from the object , using a weightless cord of length L,
we would have,
𝐼 = 𝑀𝐿2 𝑎𝑛𝑑 ℎ = 𝐿
Then, 𝑇 = 2𝜋
𝐼
𝑀𝑔ℎ
= 2𝜋
𝑀𝐿2
𝑀𝑔𝐿
= 2𝜋
𝐿
𝑔
Which is the period of a simple pendulum!

16. THANK YOU EVERYONE