When two displacements represented by y_(1)= a sin(omega t)" and "y_(2)= b cos (omega t) are superimposed the motion is…….

When two displacements represented by y_(1)= a sin(omega t)" and "y_(2

1.	When two displacements represented by y_(1)= a sin(omega t)" and "y_(2)= b cos (omega t) are superimposed the motion is…….
Answer» not a simple harmonic motion. simple harmonic with amplitude `(a)/(b)` simple harmonic with amplitude `sqrt(a^(2)+b^(2))` simple harmonic motion with amplitude `((a+b))/(2)` SOLUTION :From the both EQUATIONS of displacement it is observed that frequency for SHM are equal and the motion due to SUPERIMPOSED will be SHM Amplitude `A= sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2) cos phi)` Here, `A_(1)= a, A_(2)= b" and "cos phi = (pi)/(2)` `therefore A= sqrt(a^(2)+b^(2)+2ab cos (pi)/(2))` `therefore A= sqrt(a^(2)+b^(2))""[therefore cos (pi)/(2)=0]`.