But, wait! There is a special case where a pendulum's motion is very close to being harmonic. When the angle is less than 15 degrees or 0.26 radians, the sine of the angle is roughly equal to the angle itself. This means that the restoring force F is approximately equal to minus mg . Since the displacement s equals L times theta, the restoring force can be written as F is equal to minus mg over L times s. Because m, g and L are all constant this expression has the form of Hooke's Law, F equals minus k times the displacement x. Therefore, when the angle is less than 15 degrees or 0.26 radians the swinging pendulum exhibits simple harmonic motion Using the fact that 180 degrees equals pi radians, how many radians equal 12 degrees? ... How many radians make up 8 degrees, what is the value of sine of this angle? ... 8.0 degrees equals 0.044 radians and the sin of 0.044 radians is 0.044. So we can conclude that the sin of a small angle is equal to that angle. Just remember to use radians.

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