The displacement of a particle executing simple harmonic motion is given by y= A_(0) +A sin omega t+ B cos omega t. Then the amplitude of its oscillation is given by:

The displacement of a particle executing simple harmonic motion is giv

1.	The displacement of a particle executing simple harmonic motion is given by y= A_(0) +A sin omega t+ B cos omega t. Then the amplitude of its oscillation is given by:
Answer» `A + B` `A_(0) + sqrt(A^(2) + B^(2))` `sqrt(A^(2) + B^(2))` `sqrt(A_(0)^(2) + (A +B)^(2))` SOLUTION :`y= A_(0) + A sin omega t+ B cos omega t` Suppose `X= A sin omega t + B cos omega t` and TAKING `A= a cos phi and B= a sin phi`, `x= a sin omega t cos phi + a cos omega t sin phi` `=a [sin omega t cos phi + cos omega t sin phi]` `=a sin (omega t + phi)` and `A^(2) + B^(2) = a^(2) cos^(2) phi + a^(2) sin^(2) phi` `=a^(2) [cos^(2) phi + sin^(2) phi]` `=a^(2)` `sqrt(A^(2) + B^(2))=a` `:. y= A_(0) + x = [A_(0) + sqrt(A^(2) + B^(2))] sin (omega t + phi)` Comparing above equation with `y= A sin (omega t + phi)` AMPLITUDE `A.= A_(0) + sqrt(A^(2) + B^(2))`