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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Chapter1: Units, Trigonometry. And Vectors
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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
Transcribed Image Text: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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