Question

A body executes SHM under the influence to one force and has time period ${}^{\prime }{T}_1^{\prime }$ seconds and the same body executes SHM with period ${}^{\prime }{T}_2^{\prime }$ seconds when under the influence of another force. When both forces act simultaneously and in the same direction then the time period of the same body is?

• A. $(T_1+T_2)\sec$
• B. $\sqrt{T_1^2+T_2^2}\sec$
• C. $\sqrt{\frac{T_1+T_2}{T_1{T}_2}}\sec$
• D. $\sqrt{\frac{T_1^2{T}_2^2}{(T_1^2+T_2^2)}}\sec$

Answer 1

The correct option is D $\sqrt{\frac{T_1^2{T}_2^2}{(T_1^2+T_2^2)}}\sec$

Under the force$F_1$ time oscillation of the body $T_1$

$F_1=M{\left(\frac{2\pi }{T_1}\right)}^{2}V;whereMisthemassandvisthevelocityand{F}_2=M{\left(\frac{2\pi }{T_2}\right)}^{2}V$

$F_{Net}=F_1+F_{2}M{\left(\frac{2\pi }{T}\right)}^2=M{\left(\frac{2\pi }{T_1}\right)}^2+M{\left(\frac{2\pi }{T_2}\right)}^2\frac{1}{T^2}=\frac{1}{T_1^2}+\frac{1}{{T_2}^2}=\frac{T_1^2+T_2^2}{T_1^2{T}_2^2}=\frac{T_1{T}_2}{\sqrt{T_1^2+T_2^2}}$