Complex harmonic oscillator
The displacement and velocity of a harmonic oscillator can be represented as a complex function of time. In this applet, the displacement and velocity are represented as blue and red vectors (phasors) in the argand diagram (left). Animate the diagram by clicking on the play button in the lower left. Alter the amplitude and frequency ()of the oscillator using the sliders.
The right hand plot shows the temporal behaviour of the real part of each complex function. The real part of the phasors for displacement and velocity are shown by the blue and red points.
You may introduce a damping constant by increasing its value on the slider. Note what happens to the temporal behaviour of the displacement and velocity when you do so. Also note the phase difference between the displacement and velocity.