A simple pendulum. An idealized simple pendulum is given by a mass m hanging fro

Question

A simple pendulum. An idealized simple pendulum is given by a mass m hanging from a massless string of length L. Its motion is described by the angle theta(t), where t is time. The distance travelled by the pendulum is the arclength s(t) = L theta(t). According to Newton's 2nd law, the pendulum mass X acceleration equals the restoring force Fnet acting on it. where Fnet = mg sin theta (see picture). For small angles one often uses the approximation sin theta theta to replace this differential equation by the simpler equation (which is easy to solve, as you'll find out in Math 316). Question: If the angle swings with pi/10 ? theta ? pi/10, what is an upper bound for the error made in the approximation

Explanation / Answer

Sin pi/10 =0.309016 pi/10=0.3141592 diff = 0.0051422 percentage error = 0.0051422/0.309016 = 1.664 % error

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