Question

A mass is suspended separately by two different springs in successive order then time periods is $ t_1$ and $t_2 $ respectively. If it is connected by both spring as shown in figure then time period is $t_0$, the correct relation is

• A. $ t_0^2 = t_1^2 + t_2^2 $
• B. $ t_0^{ - 2} = t_1^{ -2} + t_2^{-2} $
• C. $ t_0^{ - 1} = t_1^{ - 1} + t_2^{ - 1} $
• D. $ t_0 = t_1 + t_2 $

Answer 1

Answer: (B)

$\because T =2 \pi \sqrt{\frac{ m }{ K }}$
$ \Rightarrow K \propto \frac{1}{ T ^{2}}$
In this case $ K = K _{1}+ K _{2}$
$\frac{1}{ t _{0}^{2}}=\frac{1}{ t _{1}^{2}}+\frac{1}{ t _{2}^{2}}$
$ \Rightarrow t _{0}^{-2}= t _{1}^{-2}+ t _{2}^{-2}$