Spring mass system is shown in figure. Find the elastic potential energy stored in each spring when block is at its mean position. Also find the time period of vertical oscillations. The system is in vertical plane.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
, 
and 
from above, time period = 2 π 
Sol. Let at equilibrium, elongation in springs are x 1 , x 2 and x 3 then by force balance
3kx 3 = Mg = 2kx 2 = k x 1
⇒ x 1 = 
; x 2 = 
; x 3 = 
So potential energy stored in each spring
(P.E.) 1 = 
kx 1 2 = 
(P.E.) 2 = 
2kx 2 2 = 
(P.E.) 3 = 
3kx 3 2 = 
and Net spring constant = 
= 
So Time period = 2 π 
= 2 π 
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