A body executes SHM of period `3s` under the influence of one force, and SHM of period `4s` under the influence of a second force. When both the forces act simultaneously in the same direction, the period of oscillation will be

Options

A. `7s`
B. `5s`
C. `2sqrt3s`
D. `2.4s`

Answer

D

Explanation

`F_1=-k_1x`, `omega_1=sqrt(k_1/m)`
`F_2=-k_2x`, `omega_2=sqrt((k_1)/(m))`
`F_3=F_1+F_2=-(k_1+k_2)x`, `omega=sqrt((k_1+k_2)/(m))`
`omega^2=(k_1+k_2)/(m)=omega_1^2+omega_2^2`
`(1)/(T^2)=(1)/(T_1^2)+(1)/(T_2^2)`
`T=(T_1T_2)/(sqrt(T_1^2+T_2^2))=(3xx4)/(sqrt(3^2+4^2))=(12)/(5)=2.4s`