Due to some force `F_(1)` a body oscillates with period `4//5s` and due to other force `F_(2)` it oscillates with period `3//5s`. If both the forces acts simultaneously in same direction then new period is

Options

A. 0.72 s
B. 0.64 s
C. 0.48 s
D. 0.36 s

Answer

C

Explanation

`F = F_(1) + F_(2) = m omega_(1)^(2)x + m omega_(2)^(2) x = m omega^(2) x`
`rArr theta = sqrt(omega_(1)^(2) + omega_(2)^(2))`
`rArr T = (T_(1)T_(2))/(sqrt(T_(1)^(2) + t_(2)^(2))) = ((4)/(5) xx (3)/(5))/(sqrt(((4)/(5))^(2) + ((3)/(5))^(2))) = (12)/(25) = 0.48 s`