The displacement of a particle varies with time according to the relation y= a sin omega t+b cos omega t……………

The displacement of a particle varies with time according to the relat

1.	The displacement of a particle varies with time according to the relation y= a sin omega t+b cos omega t……………
Answer» the motion is oscillatory but not SHM the motion is SHM with AMPLITUDE `a+b` the motion is SHM with amplitude `(a^(2)+ b^(2))` the motion is SHM with amplitude `sqrt((a^2)+(b^2))` SOLUTION :`y= a SIN omega t+b cos omega t` comparing `y= A sin omega t cos phi +A cos omega t sin phi` `therefore a= A sin phi " and "b= A cos phi` `therefore a^(2)+ b^(2)= A^(2) (cos^(2) phi + sin^(2)phi)= A^(2)` `therefore A= sqrt((a^2)+(b^2))` `implies y= a sin omega t+ b cos omega t` `= A sin omega t sin phi + A cos omega t cos phi` `= A sin (omega t +phi)` `(dy)/(dx)= A omega cos (omega t +phi)` and `(d^(2)y)/(dt^(2))= -A omega^(2) sin (omega t+phi)` `= -omega^(2) (A sin omega t+phi)` `therefore a = -omega^(2)y` Hence it is EQUATION of SHM with amplitude `A= sqrt(a^(2)+b^(2))`.