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Question

Two identical springs of spring constant K, each are connected in series and parallel as shown with a mass m. If the mass is slightly disturbed then the ratio of their frequencies of vertical oscillation will be


  1. 1 : 3
  2. 2 : 1
  3. 4 : 1
  4. 8 : 1


Solution

The correct option is B 2 : 1
For a suspended spring;
T=2πmKeq
Caes-1: When spring is connected in series connection
T1=2πmK1 .....(1)
Where, 1K1=1K+1K
K1=K2
on putting (1) equation (1)
T1=2πmk2
Case-2:
When spring is connected in parallel connection.
T2=2πmK2 .....(2)
Where, K2=K+K=2K
putting k2 value in equation (2)
T2=2πm2K
On dividing equation  (1) by (2)
T1T2=41=2:1
 

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