A mass `m` is suspended separately by two different springs of spring constant `k_(1)` and `k_(2)` given the time period `t_(1)` and `t_(2)` respectively. If the same mass `m` is shown in the figure then time period `t` is given by the relation

Options

A. `t=t_(1)+t_(2)`
B. `t=(t_(1).t_(2))/(t_(1)+t_(2))`
C. `t^(2)=t_(1)^(2)+t_(2)^(2)`
D. `t^(-2)=t_(1)^(-2)+t_(2)^(-2)`

Answer

D

Explanation

`t_(1)=2pisqrt((m)/(K_(1))) and t_(2)=2pisqrt((m)/(K_(2)))`
`K_(eq)=K_(1)+K_(2)`
`therefore t=2pisqrt((m)/(K_(1)+K_(2)))implies (1)/(t_(2))=(1)/(4pi^(2))((K_(1))/(m)+(K_(2))/(m))`
`implies (1)/(t^(2))=(1)/(t_(1)^(2))+(1)/(t_(2)^(2)) implies t^(-2)=t_(1)^(-2)+t_(2)^(-2)`.