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  4. A spring balance has a scale that reads from 0 to 60 kg . The length of the scale is 30 cm . A body suspended from this balance and when displaced and released, oscillates with a period of 0.8 s, what is the weight of the body when oscillating?

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Q. A spring balance has a scale that reads from $ 0 $ to $ 60\,kg $ . The length of the scale is $ 30\,cm $ . A body suspended from this balance and when displaced and released, oscillates with a period of $ 0.8\,s, $ what is the weight of the body when oscillating?

J & K CETJ & K CET 2014Oscillations

Solution:

Time period of the spring-mass system
$ T=2\pi \sqrt{\frac{m}{k}} $ .(i)
$ \Rightarrow $ For spring $ mg=kx $
$ k=\frac{mg}{x}=\frac{60\times 9.8}{30\times 10^{-2}}$
$=1960\,N/m $ ..(ii)
$ \Rightarrow $ From Eqs. (i) nd (ii)
$ 0.8=2\pi \sqrt{\frac{m}{1960}} $
$ \Rightarrow $ $ \frac{0.8\times 0.8\times 1960}{4{{\pi }^{2}}}=m $
$ m=31.81\,kg $
$ w=318.1\,N $