When a particle is performing SHM of time period T_1 the force acting on it is F_1 for a certain displacement. When the same particle is performing SHM of time period T_2 the force acting is F_1 for the same displacement. What will be the time period of the particle when a combined force of F_1 and F_2 produces the same displacement in SHM?

When a particle is performing SHM of time period T_1 the force acting

1.	When a particle is performing SHM of time period T_1 the force acting on it is F_1 for a certain displacement. When the same particle is performing SHM of time period T_2 the force acting is F_1 for the same displacement. What will be the time period of the particle when a combined force of F_1 and F_2 produces the same displacement in SHM?
Answer» SOLUTION :`F_1 = K_1 X , F_2 = - K_2 x, F_1 + F_2 =- KX impliesK = K_1 + K_2` `m omega^2 = m omega_1^2 + m omega_2^2` `implies(1)/(T_2) = 1/(T_1^2) + 1/(T_2^2) ` (or) `T^2 = (T_1^2 T_2^2)/(T_1^2 + T_2^2) and T= (T_1 T_2)/(sqrt(T_1^2 + T_2^2))`