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An unusual pendulum is made by fixing a string to a
Chapter 5, Problem 5.4(choose chapter or problem)
An unusual pendulum is made by fixing a string to a horizontal cylinder of radius R, wrapping the string several times around the cylinder, and then tying a mass m to the loose end. In equilibrium the mass hangs a distance \(l_{\mathrm{o}}\) vertically below the edge of the cylinder. Find the potential energy if the pendulum has swung to an angle \(\phi\) from the vertical. Show that for small angles, it can be written in the Hooke's law form \(U=\frac{1}{2} k \phi^{2}\). Comment on the value of k.
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QUESTION:
An unusual pendulum is made by fixing a string to a horizontal cylinder of radius R, wrapping the string several times around the cylinder, and then tying a mass m to the loose end. In equilibrium the mass hangs a distance \(l_{\mathrm{o}}\) vertically below the edge of the cylinder. Find the potential energy if the pendulum has swung to an angle \(\phi\) from the vertical. Show that for small angles, it can be written in the Hooke's law form \(U=\frac{1}{2} k \phi^{2}\). Comment on the value of k.
ANSWER:Step 1 of 4
The diagram of an unusual pendulum can be shown as,
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Review this written solution for 101714) viewed: 977 isbn: 9781891389221 | Classical Mechanics - 0 Edition - Chapter 5 - Problem 5.4
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