Two simple harmonic motions y_1= A sin omega t and y_2 = A cos omega tare superimposed on a particle of mass m. Find the total mechanical energy of the particle.

Two simple harmonic motions y_1= A sin omega t and y_2 = A cos omega t

1.	Two simple harmonic motions y_1= A sin omega t and y_2 = A cos omega tare superimposed on a particle of mass m. Find the total mechanical energy of the particle.
Answer» Solution :PHASE difference between the two SHMS is `90^@` THEREFORE, resultant amplitude is `A= sqrt(2A), E=1/2 momega^2 A_R^2 = 1/2 m omega^2 (sqrt2 A)^2 - m omega^2 A^2`