The bob of simple pendulum of length ' L ' is released from a position of small angular displacement θ. Its linear displacement at time ' t ' is ( g = acceleration due to gravity) (a) Lθcos [√(g/L) · t] (b) Lθsin [2π√(g/L) · t] (c) Lθcos [2π√(g/L) · t] (d) Lθsin [√(g/L) · t]

Answer: (a). Released from rest at the extreme, so the motion starts at maximum displacement: x = Acos ω t. Amplitude (arc) A = Lθ and ω = √(g/L). x = Lθcos [√(g/L) t] So the answer is (a).

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Simple Pendulum

The bob of simple pendulum of length ' $L$ ' is released from a position of small angular displacement $\theta$ . Its linear displacement at time ' $t$ ' is ( $g =$ acceleration due to gravity)

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Answer: (a)

Released from rest at the extreme, so the motion starts at maximum displacement: $x = A\cos\omega t$ .
Amplitude (arc) $A = L\theta$ and $\omega = \sqrt{\frac{g}{L}}$ .
$x = L\theta\cos\left[\sqrt{\frac{g}{L}}\,t\right]$
So the answer is (a).

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