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(C) For a simple pendulum,the equation of motion is given by $\frac{d^2 	heta}{dt^2} + \frac{g}{l} \sin 	heta = 0$.For small oscillations,$\sin 	he

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slightly more than $T_0$

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(C) For a simple pendulum,the equation of motion is given by $\frac{d^2 	heta}{dt^2} + \frac{g}{l} \sin 	heta = 0$.For small oscillations,$\sin 	heta \approx 	heta$,which leads to the simple harmonic motion period $T_0 = 2 \pi \sqrt{\frac{l}{g}}$.However,for larger amplitudes (like $45^{\circ}$),we use the expansion $\sin 	heta \approx 	heta - \frac{	heta^3}{6}$.The time period $T$ for a pendulum with amplitude $	heta_0$ is given by the formula $T = T_0 \left( 1 + \frac{	heta_0^2}{16} + \dots ight)$ (where $	heta_0$ is in radians).Since $	heta_0 = 45^{\circ} = \frac{\pi}{4} 	ext{ radians}$,the term $\frac{	heta_0^2}{16}$ is positive.Therefore,the time period $T$ will be slightly more than $T_0$.

$A$ simple pendulum of length $l$ is made to oscillate with an amplitude of $45^{\circ}$. The acceleration due to gravity is $g$. Let $T_0 = 2 \pi \sqrt{l / g}$. The time period of oscillation of this pendulum will be

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