SHMHard
Question
What would be the period of the free oscillations of the system shown here if mass M1 is pulled down a little force constant of the spring is k, mass of fixed pulley is negligible and movable pulley is smooth
Options
A.
B.
C.
D.
Solution
(i) Equilibrium position determination
M1g = T → (from FBD of M1)
2T = M2g + kx0 (from FBD of M2)
∴ 2M1g = M2g + kx0
∴ kx0 = 2M1g − M2g
(ii) Displace block M1 by small disp. x by
At new displaced position
− Mgx +
M1V2 + 
Differentiating equation
− M1g
= 0⇒ − M1g + M1 a +
= 0 where a = 
)⇒ − M1g +
+ M1a + 
= 0(from equilibrium − M1g + 
= 0)Hence
∴ a =
ω2 = 
ω =
∴ T2 = 2π
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