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Physics - SHM Question with Solution | TestHub

PhysicsSHMMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

Two equal masses hung from two massless springs of spring constants $k_{1}$ and $k_{2}$ . They have equal maximum velocity when executing simple harmonic motion. The ratio of their amplitudes is

Options:

Answer:

Solution:

As the masses are executing $S H M$ the velocity, $v = a ω$

$∵ v_{1} = v_{2}$ (given)

$∴ a_{1} ω_{1} = a_{2} ω_{2}$

$\frac{a_{1}}{a_{2}} = \frac{ω_{2}}{ω_{1}}$ .....(i)

We know that the time period,

$T = 2 π \sqrt{\frac{m}{k}}$

$\frac{T}{2 π} = \sqrt{\frac{m}{k}} \Rightarrow \frac{1}{ω} = \sqrt{\frac{m}{k}}$

$\Rightarrow ω = \sqrt{\frac{k}{m}}$

$\Rightarrow ω \propto \sqrt{k}$ .....(ii)

From Equations (i) and (ii), we get

$\frac{a_{1}}{a_{2}} = \sqrt{\frac{k_{2}}{k_{1}}}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:SHMSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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