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Two springs are joined and attached to a...

Two springs are joined and attached to a mass of 16 kg. The system is then suspended vertically from a rigid support. The spring constant of the two springs are `K_(1)` and `K_(2)` respectively. The period of vertical oscillations of the system will be:

A

`1/(8pi) sqrt(K_(1) + K_(2))`

B

`8pi sqrt((K_(1) + K_(2))/(K_(1)K_(2))`

C

`pi/2sqrt(K_(1)-K_(2))`

D

`pi/2sqrt(K_(1)/K_(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
the two springs are in series. Therefore, the period,
`T = 2pi sqrt(M/K) = 2pi sqrt(M((K_(1) + K_(2))/(K_(1)K_(2)))` As `M = 16 kg, T = 8pi sqrt((K_(1) + K_(2))/(K_(1)K_(2)))`
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