First slide

Applications of SHM

Question

A mass m is suspended separately by two different springs of spring constant K₁ and K₂ gives the time-period $t_{1}$ and $t_{2}$ respectively. If same mass m is connected by both springs as shown in figure then time-period t is given by the relation

Moderate

A

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

$t = \frac{t_{1} . t_{2}}{t_{1} + t_{2}}$
C

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

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

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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