First slide

Simple hormonic motion

Question

A mass m is attached to two springs of same force constant in accordance with the following four configurations. Let T₁.,, $T_{2}, T_{3}$ and T₄ be the time
periods respectively. In which combination, the time period is largest

Moderate

A

(i)
B

(ii)
C

(iii)
D

(iv)

Solution

The two springs are in parallel
$k_{p} = k_{1} + k_{2} = k + k = 2 k T_{1} = T_{3} = 2 Ï \sqrt{(\frac{m}{2 k})} The two springs are in series \frac{1}{k_{s}} = \frac{1}{k} + \frac{1}{k} = \frac{2}{k} or k_{s} = \frac{k}{2} T_{2} = 2 Ï \sqrt{\frac{2 m}{k}} T_{4} = 2 Ï \sqrt{(\frac{m}{k})}$

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