The displacement of a particle executing simple harmonic motion is given by y=A0 + A sin ωt + B cos ωtThen, the amplitude of its oscillation is given by

The displacement of given particle is                         y=A0 + A sin ωt + B cos ωt                   … (i)The general equation of SHM can be given as                         x = a sin ωt + b cos ωt                           … (ii)So, from Eqs. (i) and (ii), we can say that A0 be the value of mean position, at which y = 0.∴  Amplitude,    R = A2+B2+2AB cos θAs two functions sine and cosine have phase difference of 90o.∴                   R = A2+B2                                     (∵ cos 90°=0)