Two simple harmonic motions with the same frequency act on a particle at right angles i.e, along x and y axis. If the two amplitudes are equal and the phase difference is (pi)/(2) the resultant motion will be :

Two simple harmonic motions with the same frequency act on a particle

1.	Two simple harmonic motions with the same frequency act on a particle at right angles i.e, along x and y axis. If the two amplitudes are equal and the phase difference is (pi)/(2) the resultant motion will be :
Answer» a circle an ellipse with the major axis along y-axis an ellipse with the major axis along y-axis an STRAIGHT line inclined at `45^(@)` to the x-axis Solution :Equation of two simple harmonic motion `Y=A sin (OMEGAT+ phi) ""....(1)` `x= A sin (omega+phi+(pi)/(2))` `x=A cos (omegat+phi) ""....(2)` On squaring and adding EQUATIONS (1) & (2) . `x^(2)+y^(2)=A^(2)` This is an equation of a circle. HENCE, RESULTING motion will be a circle motion.