Question

Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure).When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is :

(1)  \(2\pi\sqrt{\frac mk}\)

(2) \(\pi\sqrt{\frac{m}{2k}}\)

(3) \(3\pi\sqrt{\frac{m}{2k}}\)

(4) \(\pi\sqrt{\frac mk}\)

Answer 1

Correct option  is (4) \(\pi\sqrt{\frac mk}\)

(4) For parallel combination \(k_{eq}=k_1+k_2\)

\(k_{eq}=4k\)

\(T=2\pi\sqrt{\frac{m}{k_{eq}}}\)