First slide

Simple hormonic motion

Question

A particle at the end of a spring executes simple harmonic motion with a period t₁ ,while the corresponding period for another spring is t₂.If the period of oscillation with the two
springs in series is T, then :

Easy

A

$T = t_{1} + t_{2}$
B

$T^{2} = t_{1}^{2} + t_{2}^{2}$
C

$T^{- 1} = t_{1}^{- 1} + t_{2}^{- 1}$
D

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

Solution

$t_{1} = 2 π \sqrt{\frac{M}{k_{1}}}, t_{2} = 2 π \sqrt{\frac{m}{k_{2}}} and T = 2 π \sqrt{\frac{M}{k_{eff}}}$
When springs are connected in series,
$\frac{1}{k_{eff}} = \frac{1}{k_{1}} + \frac{1}{k_{2}} \Rightarrow T^{2} = t_{1}^{2} + t_{2}^{2}$

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