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A particle has a time period of 1s under the action of a certain force and 2 s under the action of another force. Find the time period when the forces are acting in the same direction simultaneously.

Answer» <html><body><p></p>Solution :<a href="https://interviewquestions.tuteehub.com/tag/let-11597" style="font-weight:bold;" target="_blank" title="Click to know more about LET">LET</a> the period of oscillation be `T_1`under tre action of the force `F_1 and T_2`under the action of force `F_2`when acting <a href="https://interviewquestions.tuteehub.com/tag/separately-7264663" style="font-weight:bold;" target="_blank" title="Click to know more about SEPARATELY">SEPARATELY</a>. Lot F be the <a href="https://interviewquestions.tuteehub.com/tag/resultant-1187362" style="font-weight:bold;" target="_blank" title="Click to know more about RESULTANT">RESULTANT</a> force and the period of oscillation under the action of the resultant force <br/> `F=F_1+F_2` <br/> `momega^2y= momega_1^2y+momega_2^2y` <br/> `((2pi)/T)^2=((2pi)/T_1)^2+((2pi)/T_2)^2` <br/> `1/T^2=1/T_1^2+1/T_2^2` <br/> `T^2=(T_1^2T_2^2)/(T_1^2+T_2^2)` <br/> `T=(T_1T_2)/(<a href="https://interviewquestions.tuteehub.com/tag/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a>(T_1^2+T_2^2))` <br/> `T_1=1 s, T_2 = <a href="https://interviewquestions.tuteehub.com/tag/2s-301125" style="font-weight:bold;" target="_blank" title="Click to know more about 2S">2S</a>` <br/> `T = (1xx2)/(sqrt(1^2+2^2))` <br/> = 0.894 s</body></html>


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