Question 14.7: A simple pendulum consists of a mass hanging on the end of a...
A simple pendulum consists of a mass hanging on the end of a light inextensible string.
The angle θ radians between the string and the vertical satisfies the differential equation
i) Find the length of the pendulum for which the period for small oscillations is 2 s.
The pendulum is released when the string makes an angle of 0.2 rad with the vertical.
ii) Find an equation for θ in terms of t.
iii) Find the times when the pendulum is in the equilibrium position.
iv) Find also the time taken for the pendulum to move from the equilibrium position to a point half-way to the end of the oscillation.
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