Question

The vibration of the machine is expressed as the rectangular form x(t) = -3sin5t - 2cos5t mm. Determine the amplitude and phase of the vibration, if this is to be expressed as the harmonic Amplitude-Phase form of x(t) = Acos(5t+phi), where A the amplitude and phi is the phase of the vibration.

Answer 1

Given that x(t) = -3 sin 5t - 2 cos 5t mm This is in the form x(t) = A sin wt + b cos wt where A = -3, B = -2, w = 5 amplitude a = squareroot A^2 + b^2 = squareroot (-3)^2 + (-2)^2 = 3.6mm phase pi = tan^-1(B/A) = tan^-1(-2/-3) = 0.588 Therefore x(t) = 3.6 cos(5t + 0.588)