13. A simple pendulum consists of a point mass m suspended by a (weightless) cord or rod of length l, as shown, and swinging in a vertical plane under the action of gravity. Show that for small oscillations (small 0), both 0 and r are sinusoidal functions of time, that is, the motion is simple harmonic. Hint: Write the differential equation F = ma for the particle m. sin 0 = 0 for small 0, and show that 0 = Asin wt is a solution of your equation. What are A and w? Use the approximation m

13. A simple pendulum consists of a point mass m suspended by a (weightless) cord or rod of length l, as shown, and swinging in a vertical plane under the action of gravity. Show that for small oscillations (small 0), both 0 and r are sinusoidal functions of time, that is, the motion is simple harmonic. Hint: Write the differential equation F = ma for the particle m. sin 0 = 0 for small 0, and show that 0 = Asin wt is a solution of your equation. What are A and w? Use the approximation m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

13. A simple pendulum consists of a point mass m suspended by a
(weightless) cord or rod of length l, as shown, and swinging in
a vertical plane under the action of gravity. Show that for small
oscillations (small 0), both 0 and r are sinusoidal functions of time,
that is, the motion is simple harmonic. Hint: Write the differential
equation F = ma for the particle m.
sin 0 = 0 for small 0, and show that 0 = Asin wt is a solution of
your equation. What are A and w?
Use the approximation
m

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