Question

Find the time Period of the given spring block system.
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Answer 1

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$\huge{\underline{\sf{\red{Answer\leadsto 2\pi\sqrt\dfrac{11}{6k}}}}}$

Given:

Mass = m

Spring

$k_1 = k \\ \\ k_2= 2k \\ \\ k_3 = 3k$

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$\large{\underline{\sf{\blue{Formula}}}}$

• $\dfrac{1}{k_eq} = \dfrac{1}{k_1} + \dfrac{1}{k_2} + \dfrac{1}{k_3}$
• $T=2\pi{\sqrt{\dfrac{m}{k}}}$

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Solution:

$\implies$ $\dfrac{1}{k} +\dfrac{1}{2k} + \dfrac{1}{3k}$

$\implies$ $\dfrac{1}{k} \bigg(\dfrac{6+2+3}{6}\bigg)$

$\implies$ $\dfrac{1}{k_eq} = \dfrac{11}{6k}$

$\leadsto$$k_eq=\dfrac{6k}{11}$

By Formula

$\huge{\boxed{\boxed{2\pi \sqrt\dfrac{11m}{6k}}}}$

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