Solution Found!
A simple pendulum consists of a point mass m suspended by a (weightless) cord or rod of
Chapter 7, Problem 13(choose chapter or problem)
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 ), both and x are sinusoidal functions of time, that is, the motion is simple harmonic. Hint: Write the differential equation F = ma for the particle m. Use the approximation sin = for small , and show that = A sin t is a solution of your equation. What are A and ?
Questions & Answers
QUESTION:
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 ), both and x are sinusoidal functions of time, that is, the motion is simple harmonic. Hint: Write the differential equation F = ma for the particle m. Use the approximation sin = for small , and show that = A sin t is a solution of your equation. What are A and ?
ANSWER:Step 1 of 3
Refer to the picture provided by the problem. The component of the force perpendicular to the rope is:
For small angles 
