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Calculating the speed of a swinging pendulum bob

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The linear displacement from equilibrium is s , the length of the arc. Pendulums are in common usage. For small displacements, a pendulum is a simple harmonic oscillator. A simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in Figure 1. Exploring the simple pendulum a bit further, we can discover the conditions under which it performs simple harmonic motion, and we can derive an interesting expression for its period.
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Energy of a Pendulum

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When does a pendulum bob move fastest and why?

The gravitational potential energy of an object is related to its mass and the vertical height to which the object is lifted. It can be expressed by the following formula:. You can see from the formula that the greater the weight and the higher the position of the ball, the greater the potential energy. The kinetic energy of an object in motion is related to the mass of object m and its velocity v. This mathematical relationship is expressed as:. It contiunes swinging back and forth. During this swinging, there is constant exchange between potential and kinetic energy.
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Equations for a Simple Pendulum

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First Name. Derive a formula for the maximum speed v of a simple pendulum bob in terms of g, the length L, and the maximum angle of swing theta. As shown in the figure, a bullet of mass m and speed v passes completely through a pendulum bob of mass M.
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