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Physics

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Simple Pendulum

### 15.8: Simple Pendulum

A simple pendulum consists of a small diameter ball suspended from a string, which has negligible mass but is strong enough to not stretch. In our daily life, pendulums have many uses, such as in clocks, on a swing set, and on a sinker on a fishing line.

The period of a simple pendulum depends on two factors: its length and the acceleration due to gravity. The period is completely independent of any other factors, such as mass or maximum displacement. For small displacements, a pendulum is identical to a simple harmonic oscillator, and the period of a pendulum is nearly independent of amplitude, especially if θ is less than approximately 15°. Applying Newton's second law for rotational systems, the equation of motion for a pendulum is obtained.

As an example, consider two simple pendulums suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10 kg. Pendulum 2 has a bob with a mass of 100 kg. Describe how the motion of the pendulums will differ if the bobs are both displaced by 12°.

Since the mass of the bob has no effect on the motion of a simple pendulum, the movement of the pendulums will not differ at all. A pendulum’s motion is only affected by the period (which is related to the pendulum’s length) and by the acceleration due to gravity.

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