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Normal Reaction

The condition...

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

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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Similar questions

Q. The condition, if the frictional force on block

m_{2}

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

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

m_{2}

m_{1}

μ

. There is no friction between

m_{1}

and surface. If the blocks are displaced slightly, they perform SHM together.
then, the
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(2) condition if the frictional force on block

m_{2}

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\frac{m_{1}}{m_{2}} > \frac{k_{1}}{k_{2}}

(3) If the condition obtained in (b) is met, the maximum amplitude of their oscillations is

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Normal Reaction

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