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Question

The condition if the frictional force on block $m_{2}$ is to act in the direction of its displacement from mean position.

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Solution

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Suppose the system is displaced towards left by a distance x.
Restoring force on $m_{1}$ :
$F = m_{1} ω^{2} x$ (towards right)
$= m_{1} (\frac{k_{1} + k_{2}}{m_{1} + m_{2}}) x$
Friction f on it will be towards right if,
$k_{1} x < F$
or $k_{1} x < m_{1} (\frac{k_{1} + k_{2}}{m_{1} + m_{2}}) x$
or $\frac{k_{1}}{k_{2}} < \frac{m_{1}}{m_{2}}$

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Q1

The condition if the frictional force on block

m_{2}

is to act in the direction of its displacement from mean position.

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Q2

The condition, if the frictional force on block

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is to act in the direction of its displacement from the mean position is met, what can be maximum amplitude of their oscillations?

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Q3

In the arrangement shown, both the springs are in their natural lengths. The coefficient of friction between

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