JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Elasticity & SHM

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As per given figures, two springs of spring constants K and 2K are connected to mass m. If the period of oscillation in figure (a) is 3 s, then the period of oscillation in figure (b) will be

x

s. The value of

x

is ______.

Answer: 2

Solution

For figure (a) (springs in series):

K_{e q} = \frac{K \times 2 K}{K + 2 K} = \frac{2 K}{3}

T = 2 π \frac{m}{K _{e q}} = 2 π \frac{3 m}{2 K} = 3 s

For figure (b) (springs in parallel):

K_{e q} = K + 2 K = 3 K

T^{'} = 2 π \frac{m}{3 K}

Taking the ratio:

\frac{T ^{'}}{T} = \frac{m \times 2 K}{3 K \times 3 m} = \frac{2}{9} = \frac{2}{3}

T^{'} = 3 \times \frac{2}{3} = 2 s

Therefore,

x = 2

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Integer answer

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