Question #278636

When a pendulum of length 10 cm has swung so that π is the radian measure of the angle formed by the pendulum and a vertical line, then if β(π) cm is the vertical height of the end of the pendulum above its lowest position, β(π) = 20 π ππ^2 π/2 . Find the instantaneous rate of change of β(π) with respect to π when (a) π = π/3 and (b) π = π/2

Expert's answer

h = L (1-cos T) geometry exact

cos 2A = 1 - 2 sin^2 A identity

so

cos T = 1 - 2 sin^2 (T/2)

h = L [ 1 - (1 -2 sin^2 (T/2) ]

= L [2 sin^2 (T/2) ]

= 20 sin^2 (T/2)

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