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PART - 2 CH - 13 Oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 13 Oscillations2 Marks
Question
Two pendulum of length 1.00 and 1.1025 meters start vibrating simultaneously. After how many oscillations will they start oscillating together again ?
✓

Answer

Let the period of both length be $T_1$ and $T_2$. To oscillate together again, there must be a difference of 1 between two oscillations. If the big pendulum oscillation in this time interval then the oscillations of the small pendulum will be $(n+1)$, i.e.
$n T_2=(n+1) T_1\ldots\dots (1)$
As per question
$T_1=2 \pi \sqrt{\frac{l_1}{g}}$
$\begin{aligned}T_2 & =2 \pi \sqrt{\frac{l_2}{g}} \\\therefore \quad \frac{T_1}{T_2} & =\sqrt{\frac{l_1}{l_2}}=\sqrt{\frac{1.00}{1.1025}}=\frac{1}{1.05} \\\frac{T_1}{T_2} & =\frac{1}{1.05}\ldots \ldots (2)\end{aligned}$
From the equation (1) and (2)
$\begin{aligned}\frac{n}{n+1} & =\frac{1}{1.05} \\1.05 n & =n+1 \\1.05 n-n & =1 \\0.05 n & =1 \\n & =\frac{1}{0.05} \text { so, } n=20\end{aligned}$
Hence, 20 of the big pendulum and after 21 oscillations of the small pendulum they will oscillate together again.

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