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16.4 The Simple Pendulum

- A child is on a swing.

- The point of the wave is either at the top or the bottom of the curve.

- Hang mass from springs.
- You can slow it down.
- The lab should be transported to different planets.
- The chart shows the potential and thermal energy of the spring.

- A simple pendulum has a small bob and a string that is strong enough not to stretch.
- The length of the arcs is the linear displacement from equilibrium.
- The forces on the bob result in a net force of the equilibrium position.

- Pendulums are used a lot.
- Some are important, such as in clocks, others are fun, such as a child's swing, and some are just there.
- A pendulum can be used for small displacements.
- We can find out more about the conditions under which the simple pendulum works, and we can come up with an interesting expression for its period.

- The displacement is the length of the arcs.
- The net force on the bob is related to the arcs in Figure 16.14.

- The component is canceled by the tension in the string.

- If we can show that the restoring force is proportional to the displacement, then we have a simple harmonic oscillator.

- The displacement is proportional.

- The restoring force is proportional to the displacement for angles less than about.

- The period of a pendulum can be found using this equation.

- The result is simple.
- The period of a simple pendulum can only be affected by its length and acceleration due to gravity.
- The period is not related to mass.
- The period for a pendulum is almost always independent of the amplitude.
- Simple pendulum clocks can be adjusted.

- The dependence of on is noted.
- If the length of the pendulum is known, it can be used to measure the force of gravity.
- Consider the following example.

- We are asked to find the period and length of the pendulum.
- If the angle of deflection is less than, we can solve for it.

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