Frequency of oscillation of a body is 5 Hz when a force F 1 is applied and 12 Hz when another force F 2 is applied. If both forces F 1 and F 2 are applied together, then frequency of oscillation of the body will be

Step-by-step solution

According to the question, F 1 = - k 1 x and F 2 = - k 2 x ∴ Frequency of oscillation v 1 = 1 2 π k 1 m 5 = 1 2 π k 1 m ⇒ k 1 = 100 π 2   m Similarly, 12 = 1 2 π k 2 m ⇒    k 2 = 576 π 2   m Now, F = F 1 + F 2 = - k 1 + k 2 x ∴ Frequency of oscillation, v = 1 2 π k 1 + k 2 m = 1 2 π 100 π 2 m + 576 π 2 m m ⇒    v = 13   Hz