First slide

Simple hormonic motion

Question

A block is placed on a horizontal platform. The system is making horizontal oscillations about a fixed point with a frequency of 0.5Hz. The maximum amplitude of oscillation if the block is not to slide on the horizontal platform, is (Coefficient of friction between the block and the platform = 0.4)

Easy

A

0.3971m
B

0.4871m
C

0.2971m
D

0.5271m

Solution

= KA
$\large \mu mg\, = \,m{\omega ^2}A\,\, \Rightarrow \,\mu g\, = \,{\omega ^2}A$
$\large 0.4 \times 10\, = \,{\left( {2\pi n} \right)^2}A\, \Rightarrow 4\, = \,{\left[ {2\pi \left( {0.5} \right)} \right]^2}A$
$\large 4\, = \,{\pi ^2} \times A\, \Rightarrow \,A\, = \,\frac{4}{{{\pi ^2}\,}} = \,0.397m$
$\large A\, = \,0.3971m$

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