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

Options

A. not a simple harmonic motion.
B. simple harmonic with amplitude `(a)/(b)`
C. simple harmonic with amplitude `sqrt(a^(2)+b^(2))`
D. simple harmonic motion with amplitude `((a+b))/(2)`

Answer

C

Explanation

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]`.