Two springs of spring constant k₁ and k₂ are connected by a mass m as shown in the figure. Under negligible friction, if the mass is displaced by small amount x from its equilibrium position and released, the period of oscillation is

Step-by-step solution

According to question, where, k₁= spring constant for first spring and k₂= spring constant for second spring. As, both the spring are in parallel connection, so spring constant equivalent k_p is k_p=k₁+k₂ The time period of oscillation for string mass system is given by T=2 m k_p From Eqs. (i) and (ii), we get T=2 m k₁+k₂