Oscillations

JEE Main level, numerical answer, medium

162 of 194

Question 162 of 194

In the reported figure, two bodies AandBAandB of masses 200g200g and 800g800g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _______ rads−1rad{s}^{-1} when k=20Nm−1k=20N{m}^{-{1}^{}}.

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Answer: 10

ω=keqμ\omega =\sqrt{\dfrac{{k}_{eq}}{\mu }}
μ=\mu = reduced mass
Springs are in series connection,
keq=k1k2k1+k2{k}_{eq}=\dfrac{{k}_{1}{k}_{2}}{{k}_{1}+{k}_{2}}
keq=k×4k5k=4k5{k}_{eq}=\dfrac{k\times 4k}{5k}=\dfrac{4k}{5}
keq=4×205Nm−1=16Nm−1{k}_{eq}=\dfrac{4\times 20}{5}N{m}^{-1}=16N{m}^{-1}
μ=m1m2m1+m2=0.2×0.80.2+0.8=0.16kg\mu =\dfrac{{m}_{1}{m}_{2}}{{m}_{1}+{m}_{2}}=\dfrac{0.2\times 0.8}{0.2+0.8}=0.16kg
ω=160.16=100=10\omega =\sqrt{\dfrac{16}{0.16}}=\sqrt{100}=10

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