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Two springs of force constants k1 and k2 are connected to a mass m as shown in Figs (a) and (b). What is the ratio of the time periods of vertical oscillation in cases (a) and (b) if k1 = k2?

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a

14

b

12

c

2

d

4

answer is B.

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Detailed Solution

In case (a), the springs are connected in parallel.Thereforek′=k1+k2=2k ∴Ta=2πmk′=2πm2kIn case (b), the springs are connected in series. Therefore Tb=2πmk/2∴TaTb=12

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Two springs of force constants k1 and k2 are connected to a mass m as shown in Figs (a) and (b). What is the ratio of the time periods of vertical oscillation in cases (a) and (b) if k1 = k2?