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Question

Find time period of SHM =?

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Solution

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$T_{0} = m g$
$\frac{1}{2} K h + \frac{K x}{4} - m g = m a$
$T - m g = m a$
$K (h + \frac{x}{2}) = 2 T$
$\frac{1}{2} K (h + \frac{x}{2}) - m g = m a$
$\frac{1}{2} K h + \frac{K x}{4} - m g = m a$
$a = \frac{- K}{4 m} x$
$a = - ω^{2} x ⟹ ω = \sqrt{\frac{K}{4 m}}$
$T = \frac{2 π}{ω} = 2 π \sqrt{\frac{4 m}{K}}$

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