In the given arrangement two ideal and identical springs a and b having spring constant k

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Solution : Let the mass m be displaced by a small distance x to the right as shown in figure. Due to it, the spring on the left hand side gets stretched by length x and the spring on the right hand side gets compressed by length x. The forces acting on the mass due to springs are `F_(1)=-kx` towards left hand side `F_(2)=-kx` towards left hand side Therefore, total restoring force on mass m is `F=F(1)+F_(2)=-kx+(-kx)=-2kx` ...(i) Here `-ve` sign showns that force F is directed towards the equilibrium position O and `Fpropx. ` Therefore, if the mass m i s left free, it will execute linear SHM. Comparing (i) with the relation, `F=-Kx, we have ` Spring factor, `K=2k` Here, inertia factor`=` mass of the block`=` m As time period, `T=2pisqrt((I n e r tia fact o r)/(spri ngfact o r))` `=2pisqrt((m)/(2k))`