First slide

Simple hormonic motion

Question

A mass is suspended separately by two different springs in successive order, then time period is T₁ and T₂ respectively.If it is connected by both springs as shown in Fig. then time period is T₀. The correct relation is

Moderate

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

$T_{0} = T_{1} + T_{2}$

Solution

$T = 2 π \sqrt{\frac{m}{k}} \Rightarrow k \propto \frac{1}{T^{2}}$
In parallel combination, $k = k_{1} + k_{2} \frac{1}{T_{0}^{2}} = \frac{1}{T_{1}^{2}} + \frac{1}{T_{2}^{2}}$

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