7. What is a simple pendulum ? Show that motion executed by the bob of

1.	7. What is a simple pendulum ? Show that motion executed by the bob of the pendulum is S.H.M.Derive an expression for its time period.What are free and damped oscillations? Show them graphically. 10/153 -> 18.19
Answer» Let a mass m be suspended with a string of length l and be displaced by a force F through a small angle θ. From the FBD we see that the restoring force is mgsin(θ) Since the displacing force F is acting opposite to the restoring force F = ─mgsin(θ) Now since θ is small sinθ ≈ θ Let the horizontal displacement bex θ =x/l Thus, F = ─mgθ => F = -mgx/l =>F = -(mg/l)x => F = -kx [since mg/l is a constant] Restoring force is thus directly proportional to the displacement, hence the motion is SHM for small anglesθ. F = -(mg/l)x => ma = -(mg/l)x => a = (g/l)x

7. What is a simple pendulum ? Show that motion executed by the bob of the pendulum is S.H.M.Derive an expression for its time period.What are free and damped oscillations? Show them graphically. 10/153 -> 18.19

Answer»

Let a mass m be suspended with a string of length l and be displaced by a force F through a small angle θ.

From the FBD we see that the restoring force is mgsin(θ)

Since the displacing force F is acting opposite to the restoring force

F = ─mgsin(θ)

Now since θ is small

sinθ ≈ θ

Let the horizontal displacement bex

θ =x/l

Thus,

F = ─mgθ

=> F = -mgx/l

=>F = -(mg/l)x

=> F = -kx [since mg/l is a constant]

Restoring force is thus directly proportional to the displacement, hence the motion is SHM for small anglesθ.

F = -(mg/l)x

=> ma = -(mg/l)x

=> a = (g/l)x

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