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. `(12)/(25)`
B. `(7)/(5)`
C. `(24)/(25)`
D. `(5)/(7)`

Answer

A

Explanation

`F=- momega^(2)x=-m((2pi)/(T))^(2)x`
`F prop (1)/(T^(2))So F_(1)prop(1)/(T^(2))& F_(2)prop (1)/(T_(2)^(2))`
`F_(eq)=F_(1)+F_(2)prop(1)/(T_(eq)^(2))`
`(1)/(T_(eq)^(2))=(1)/(t_(1)^(2)+(1)/(T_(2)^(2))`
`T_(eq)=(12)/(25)`