SHMHard
Question
Two springs, each of spring constant k, are attached to a block of mass m as shown in the figure. The block can slide smoothly along a horizontal platform clamped to the opposite walls of the trolley of mass M. If the block is displaced by x cm and released, the period of oscillation is :
Options
A.T = 2π
B.T = 2π
C.T = 2π
D.T = 2π
Solution
by linear momentum conservation
mv1 = Mv2 ⇒ v2 =
so x2 = 
For block Force equation can be written as
F = 2k(x1 + x2) = mω2x1
⇒ 2k
= mω2x1 ⇒ ω2 = 2k 
So T = 2π
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