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3 Questions around this concept.
Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is :
The general equation of linear SHM is given by
Similarly, The general equation of angular SHM is given by
where are angular displacement and angular amplitude of the bob respectively, as shown in the below figure
If l=length of the bob then we can write .
Similarly, The angular velocity if the bob which is in angular SHM is given by
Similarly, The angular acceleration if the bob which is in angular SHM is given by
And Thus restoring torque on the body is given as
Thus we can state that in angular SHM, the angular acceleration of the body and the restoring torque on the body are directly
proportional to the angular displacement of body from its mean position and are directed toward the mean position.
Similarly, a basic differential equation for angular SHM can be written as
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