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
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics
Section: Chapter Questions
Problem 7.14P
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