A mass is suspended separately by two springs of spring constants k 1 and k 2 in successive order. The time periods of oscillations in the two cases are T 1 and T 2 respectively. if the same mass be suspended by connecting the two springs in parallel, (as shown in figure) then the time period of oscillations is T. The correct relation is:
Text Solution
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For a vertical spring-block system time period can be written as
T = 2 π 
We can write time period for a vertical spring-block system as
T = 2 π 
Here, λ is extension in the spring when the mass m is suspended from the spring.
This can be seen as under:
k λ = mg (in equilibrium position)
⇒ 
∴ T = 
∴ T 1 = 
⇒ k 1 = 
...(i)
T 2 = 
⇒ k 2 = 
...(ii)
Since springs are in parallel, effective force constant
k = k 1 + k 2
T = 
⇒ k 1 + k 2 = 
Substituting value of k1 and k2 from Eqs. (i) and (ii) in Eq. (iii), we get
⇒ 
T –2 = 
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