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  • The motion of a simple pendulum executing S.H.M. is represented by the following equation <img alt="\small 11 \sin (6 \pi t+\varphi)" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Csmall%2

The motion of a simple pendulum executing S.H.M. is represented by the following equation \small 11 \sin (6 \pi t+\varphi) where time is measured in seconds. The length of Pendulum is 

Option: 1

0.0277 cm


Option: 2

2.0667 cm


Option: 3

3.6578 cm


Option: 4

8.9955 cm


Answers (1)

best_answer

\begin{aligned} & y=19 \sin (6 \pi t+\varphi) \\ & \omega=\frac{2 \pi}{T} \\ & 6 \pi=\frac{2 \pi}{T} \\ & 6 T=2 \\ & T=\frac{2}{6} \\ & T=\frac{1}{3} \mathrm{sec} . \end{aligned}

\begin{aligned} & T=2 \pi \sqrt{\frac{l}{g}} \\ & \frac{1}{3}=2 \pi \sqrt{\frac{l}{g}} \\ & \frac{1}{g}=\frac{4 \pi^2 l}{g} \\ & g=9 \times 4 \pi^2 \times l \\ & l=\frac{g}{9 \times 4 \times(3.14)^2} \end{aligned}

l=\frac{9.8}{36 \times 3.14 \times 3.14} =\frac{980006}{36 \times 314 \times 34 \times 16}

l=0.0277 \mathrm{~cm}

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jitender.kumar

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