Q.A particle is subjected to two parallel S.H.M.s such that x = 2 sin ωt and y = 2 sin(ωt + π/3). The amplitude of the resultant S.H.M. will be ______.

When a single particle is subjected simultaneously to two S.H.M.s of the SAME period, acting along the SAME straight-line path, but with different amplitudes A1, A2 and different initial phases phi1, phi2, the resultant motion x = x1 + x2 is itself a pure S.H.M. of that same period, x = R sin(omega t + delta), where the new amplitude and phase are found from Rcos(delta) = A1cos(phi1) + A2cos(phi2) and Rsin(delta) = A1sin(phi1) + A2sin(phi2). Squaring and adding these gives R^2 = A1^2 + A2^2 + 2A1A2*cos(phi1 - phi2); dividing them gives tan(delta) in terms of the same four quantities. …