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The motion of simple pendulum executing S.H.M. is represented by the following equation. $y = Asin (πt + ϕ),$ where time is measured in second. The length of pendulum is

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$25.3 c m$

$406.1 c m$

$99.4 c m$

$97.23 c m$

answer is C.

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Detailed Solution

$y = A \sin (π t + ϕ)$

Given $ω = π \Rightarrow T = \frac{2 π}{ω}$

$= \frac{2 π}{π} = 2$ sec

$T = 2 π \sqrt{\frac{l}{g}} \Rightarrow l = \frac{g T^{2}}{4 π^{2}}$

$= \frac{9.8 \times 2^{2}}{4 \times {(3.14)}^{2}} \approx 99.4 c m$

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