SHMMedium

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

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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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