Publish On: 2018-12-16

# Lewis anna

Total Post: 755

## Question: Describe the construction of a simple pendulum

Reply On: 2014-01-14

# lala singh

Total Post: 22

## ANS: Describe the construction of a simple pendulum

One of the most common of approximate simple harmonic motions is the motion of a pendulum. A pendulum consisting of a small relatively heavy bob at the end of a very light string is called a simple pendulum. If such as a pendulum is displaced the weight mg of the bob supplies a restoring force

F = - mg sin θ

The displacement along the arc is s = lθ. Hence, the force is proportional to sin θ, while the displacement is proportional to θ. The restoring force is not proportional to the displacement. Moreover, the restoring force is not directed toward the equilibrium position, but rather it is tangent to the arc. Thus the motion is not simple harmonic. However, if θ is small, we may replace sin θ (in radians) without serious error. To this degree of approximation the motion may be considered as simple harmonic motion. Then

F = - mg sin θ

The displacement along the arc is s = lθ. Hence, the force is proportional to sin θ, while the displacement is proportional to θ. The restoring force is not proportional to the displacement. Moreover, the restoring force is not directed toward the equilibrium position, but rather it is tangent to the arc. Thus the motion is not simple harmonic. However, if θ is small, we may replace sin θ (in radians) without serious error. To this degree of approximation the motion may be considered as simple harmonic motion. Then

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