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.

A particle has a time period of 1s under the action of a certain force

1.	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» Solution :LET 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 SEPARATELY. Lot F be the RESULTANT force and the period of oscillation under the action of the resultant force `F=F_1+F_2` `momega^2y= momega_1^2y+momega_2^2y` `((2pi)/T)^2=((2pi)/T_1)^2+((2pi)/T_2)^2` `1/T^2=1/T_1^2+1/T_2^2` `T^2=(T_1^2T_2^2)/(T_1^2+T_2^2)` `T=(T_1T_2)/(SQRT(T_1^2+T_2^2))` `T_1=1 s, T_2 = 2S` `T = (1xx2)/(sqrt(1^2+2^2))` = 0.894 s