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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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