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Two simple pendulums whose lengths are 100 ,cm and 121 ,cm are

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Two simple pendulums whose lengths are $100 c m$ and $121 c m$ are suspended side by side. their bobs are pulled together and then released. After how many minimum oscillation of the longer pendulum will the two be in phase again

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Two simple pendulums whose lengths are

100 c m

and

121 c m

are suspended side by side. their bobs are pulled together and then released. After how many minimum oscillation of the longer pendulum will the two be in phase again

15 mins ago

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Text solutionVerified

Let

T_{1}

and

T_{2}

are the time of the two pendulum

T_{1} = 2 π \frac{100}{g}

and

T_{2} π \frac{121}{g}

(T_{1} < T_{2}

because

l_{1} < l_{2})

Let at

t = 0

, they start swinging together. SInce their time periods are different, the swinging will not be in unison always. Only when number of complete oscillation differs by an integer, the two pendulum will again begin to swing together.
Let longer length pendulum complete

n

oscillation and shorter length pendulum complete

(n + 1)

oscillation for the incision swinging,

then

(n + 1) T_{1} = n T_{2}

(n + 1) \times 2 π \frac{100}{g} = n \times 2 π \frac{121}{g}

\Rightarrow n = 10

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Question Text	Two simple pendulums whose lengths are $100 c m$ and $121 c m$ are suspended side by side. their bobs are pulled together and then released. After how many minimum oscillation of the longer pendulum will the two be in phase again
Answer Type	Text solution:1
Upvotes	150

Two simple pendulums whose lengths are 100cm and 121cm are suspended side by side. their bobs are pulled together and then released. After how many minimum oscillation of the longer pendulum will the two be in phase again

Text solutionVerified

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Two simple pendulums whose lengths are $100 c m$ and $121 c m$ are suspended side by side. their bobs are pulled together and then released. After how many minimum oscillation of the longer pendulum will the two be in phase again