Suppose a pendulum with length L (meters) has angle θ (radians) from the vertical. It can be shown that θ as a function of time satisfies the differential equation:
(d^2θ/dt^2)+(g/L)sinθ=0 where g=9.8 m/sec/sec is the acceleration due to gravity. For small values of θ we can use the approximation sin(θ)∼θ, and with that substitution, the differential equation becomes linear.
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