When is the period of oscillation maximum and minimum?
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In a pendulum, when the angle that the string makes with the vertical is θ, the force of gravity on the bob, mg, can be resolved into two components, mgcosθ, along the direction of the string and mgsinθ, tangential to the path of the bob.
The tension on the string is equal in magnitude and opposite in direction to the component mgcosθ.
If θ0 is the maximum value of the angle of displacement of the string, the minimum value of the tension would be when the displacement is maximum (and the linear velocity is zero) and its magnitude would be mgcosθ0.
The maximum value of the tension would be when the displacement is zero (the pendulum is in a vertical position). and its magnitude would be mgcos0=mg.
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