A particle under the action of a force has a period of `3s` and under the action of another force it has a period `4sec` in `SHM`. What will be its period under the combined action of both forces in the same direction?

Options

A. 7 s
B. 5 s
C. 2.4 s
D. 0.4 s

Answer

C

Explanation

`T = 2 pi sqrt((m)/(k))or T prop (1)/(sqrt(k))`
T has increased `(4)/(3)` times. Hence, `k'=(9)/(16)k`.
When both are combined,
`k_("net")=k+k'=(25)/(16)k or (25)/(16)`times
Hence, new time period will become `(4)/(5)` times of 3 s or 2.4 s.