A body executes $SHM$ under the influence of one force and has a period $T_1\, second$ and the same body executes $SHM$ with period $T_2\, second$ when under the influence of another force. When bothforces act simultaneously and in the same direction, then the time period of the same body is
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Under the force $F_{1}$ time oscillation of the body $T_{1}$
$F_{1}=M\left(\frac{2 \pi}{T_{1}}\right)^{2} V ; \quad$ where $\quad M \quad$ is the mass and
$v$ is the velocity and $F_{2}=M\left(\frac{2 \pi}{T_{2}}\right)^{2} V$
$F_{N e t}=F_{1}+F_{2}$
$M\left(\frac{2 \pi}{T}\right)^{2}=M\left(\frac{2 \pi}{T_{1}}\right)^{2}+M\left(\frac{2 \pi}{T_{2}}\right)^{2}$
$\frac{1}{T^{2}}=\frac{1}{T_{1}^{2}}+\frac{1}{T_{2}^{2}}=\frac{T_{1}^{2}+T_{2}^{2}}{T_{1}^{2} T_{2}^{2}}=\frac{T_{1} T_{2}}{\sqrt{T_{1}^{2}+T_{2}^{2}}}$
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