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PhysicsSHMCalculation of time periodMedium2 minPYQ_2021

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If two similar springs each of spring constant $K_{1}$ are joined in series, the new spring constant and time period would be changed by a factor:

Answer:

Solution:

$\frac{1}{k_{e q}} = \frac{1}{k_{1}} + \frac{1}{k_{2}}$

$\frac{1}{k_{e q}} = \frac{1}{k} + \frac{1}{k} \Rightarrow k_{e q} = \frac{k}{2}$

$k^{'} = \frac{k}{2}$

$T = 2 π \sqrt{\frac{M}{k}}$

$T^{'} = 2 π \sqrt{\frac{M}{k^{'}}}$

$\Rightarrow T^{'} = 2 π \sqrt{\frac{M}{k}} \times \sqrt{2}$

$T^{'} = \sqrt{2} T$

Stream:JEESubject:PhysicsTopic:SHMSubtopic:Calculation of time period

⏱ 2mℹ️ Source: PYQ_2021

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