Problem. A simple pendulum oscillates with frequency [itex]f[/itex]. What is the frequency if it accelerates at [itex]1/2 g[/itex] (a) upward, and (b) downward?(adsbygoogle = window.adsbygoogle || []).push({});

Let [itex]m[/itex] be the mass of the bob at the end of the cord of length [itex]l[/itex] that is making an angle [itex]\theta[/itex] with the line through the point of equilibrium.

Given (a), the total net force on the bob in the vertical direction is [itex]\frac{1}{2} mg[/itex] and the component of this net force tanget to the motion of the bob is [itex]\frac{1}{2} mg \sin \theta[/itex] which is roughly [itex]\frac{1}{2} mg \theta[/itex] for small [itex]\theta[/itex]. As far is I can tell, this component is the net force tangent to the motion of the bob and since it isn't akin to Hooke's law, the pendulum is not undergoing simple harmonic motion so it has no frequency. Somehow, I feel that my analysis is wrong here. Did I overlook something?

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# Frequency of an Accelerating Pendulum

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