Question #3aa50

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Question #3aa50

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Answer 1 · 2015-07-29T10:48:05

$l = 981 cm$ $l=981" cm"$

Explanation:

The period of oscillation of a simple pendulum is obtained from the formula : $T = 2 \cdot π \cdot \sqrt{\frac{l}{g}}$ $T=2*pi*sqrt(l/g)$

And since $T = \frac{1}{f}$ $T=1/f$

We can write $\frac{1}{f} = 2 \cdot π \cdot \sqrt{\frac{l}{g}}$ $1/f=2*pi*sqrt(l/g)$

$\Rightarrow {(\frac{1}{f})}^{2} = {(2 \cdot π \cdot \sqrt{\frac{l}{g}})}^{2}$ $=>(1/f)^2=(2*pi*sqrt(l/g))^2$

$\Rightarrow (\frac{1}{f^{2}}) = 4 \cdot π^{2} \cdot \frac{l}{g}$ $=>(1/f^2)=4*pi^2*l/g$

$\Rightarrow l = \frac{\frac{g}{f^{2}}}{4 \cdot π^{2}} = \frac{\frac{981 {cm s}^{- 2}}{{(1 s^{- 1})}^{2}}}{4 \cdot π^{2}} = 24.851 cm$ $=>l=(g/f^2)/(4*pi^2)=((981" cm s"^-2)/(1" s"^-1)^2)/(4*pi^2)=color(blue)(24.851" cm")$

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Question #3aa50

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