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
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Answer 1

Given :

Mass of block = m

Mass of trolley = M

Spring constant = k

Displacement = x

To find :

The time period of oscillation = ?

Solution :

• Keff = 2k (As they are parallel)

• Reduced mass = mM/(m+M)

• Time period (T) = 2π×√(M/k)

                                  =2π×√(Mm/(M+m)2k)

                                  =2π×√(Mm/2k(M+m))

The time period of oscillation is 2π×√(Mm/2k(M+m))