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Q.

A mass m is suspended separately by two different springs of spring constant K₁ and K₂ gives the time period t₁ and t₂ respectively. If same mass m is connected by both springs as shown in figure then time period t is given by the relation

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a

$t = t_{1} + t_{2}$

b

$t = \frac{t_{1} \cdot t_{2}}{t_{1} + t_{2}}$

c

$t^{2} = t_{1}^{2} + t_{2}^{2}$

d

$t^{- 2} = t_{1}^{- 2} + t_{2}^{- 2}$

answer is D.

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Detailed Solution

$t_{1} = 2 π \sqrt{\frac{m}{K_{1}}} and t_{2} = 2 π \sqrt{\frac{m}{K_{2}}}$

Equivalent spring constant for shown combination is

K₁ + K₂. So time period t is given by

$t = 2 π \sqrt{\frac{m}{K_{1} + K_{2}}}$

By solving these equations we get

$t^{- 2} = t_{1}^{- 2} + t_{2}^{- 2}$

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A mass m is suspended separately by two different springs of spring constant K1 and K2 gives the time period t1 and t2 respectively. If same mass m is connected by both springs as shown in figure then time period t is given by the relation