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MHT CET 2023 (12 May, Shift 1) · Spring Systems

Spring Systems question from MHT CET 2023 (12 May, Shift 1)

Q47MHT CET 2023 · 12 MAY · SHIFT 1Easy

Spring Systems

Four massless springs whose force constants are $2K,\ 2K,\ K$ and $2K$ respectively are attached to a mass $M$ kept on a frictionless plane as shown in figure. If mass $M$ is displaced in horizontal direction then frequency of oscillating system is

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Answer: (b)

Left side: $2K$ and $2K$ in series, $k_L = \frac{2K \cdot 2K}{4K} = K$ .
Right side: $K$ and $2K$ side by side (parallel), $k_R = 3K$ .
Both sides act on $M$ together: $k_{eff} = K + 3K = 4K$ .
$f = \frac{1}{2\pi}\sqrt{\frac{4K}{M}}$ , so the answer is (b).

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