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Write down the potential energy U(0) of a simple pendulum

Chapter 5, Problem 5.3

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QUESTION:

Write down the potential energy U(0) of a simple pendulum (mass m, length 1) in terms of the angle 0 between the pendulum and the vertical. (Choose the zero of U at the bottom.) Show that, for small angles, U has the Hooke's law form U(0) = 4k02, in terms of the coordinate 0. What is k?

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QUESTION:

Write down the potential energy U(0) of a simple pendulum (mass m, length 1) in terms of the angle 0 between the pendulum and the vertical. (Choose the zero of U at the bottom.) Show that, for small angles, U has the Hooke's law form U(0) = 4k02, in terms of the coordinate 0. What is k?

ANSWER:

Step 1 of 3

The position of the particle at any time can be described by the angle between the string and the vertical. The mean position or the equilibrium position correspond to . In the case of the simple pendulum, if the amplitude of oscillation is very-very small then the path of the particle will be approximated as linear.  

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