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The string, the spring and the pulley sh...

The string, the spring and the pulley shown in figure are light. Find the time period of the mass m.

Text Solution

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Let in equilibrium position of the block, extension in spring is `x_(0)`.
`:. Kx_(0) = mg " " cdots (1)`
Now if we displace the block by x in the downward direction, net force on the block towards mean position is
`F k (x+x_(0))` - mg = kx using (1)
Hence the net force is acting towards mean position and is also proportional to x. So, the particle will perform S.H.M. and its time period would be
` T= 2pi sqrt((m)/(k))`
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