Two springs are connected on the opposite side of a mass m, kept on a frictionless surface. The springs are placed horizontally and, their other ends are fixed on rigid supports. If K₁ and K₂ are the force constants of the two springs, the frequency of oscillation of mass m is 

CONCEPT:

• A mass m kept on a horizontal frictionless surface and connected to a spring is in equilibrium when it is at rest and the spring is unstretched.

• Given a small disturbance, the mass starts to oscillate due to a restoring force F = Kx acting on the mass from the spring,

Where K = spring constant and x = perturbation in the position of the object.

• The frequency of oscillations performed by the mass is 

​\(\Rightarrow f=\frac{1}{2\pi}\sqrt{\frac{K}{m}}\)

EXPLANATION:

• When a mass m is connected to two springs as shown below, the system can be treated as two parallel spring systems with spring constants K₁ and K₂.

\(\Rightarrow f=\frac{1}{2\pi}\sqrt{\frac{K_1+K_2}{m}}\)

• Therefore, option 2 is correct.