Question

How is the equation of simple harmonic motion y=a sinwt derived and what is the physical meaning of phase

Answer 1

Let's derive the equation of simple harmonic motion by t:
y' = aw cos(wt).

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple harmonic motion. The same concept applies to wave motion, viewed either at a point in space over an interval of time or across an interval of space at a moment in time. Simple harmonic motion is a displacement that varies cyclically, as depicted to the right.
It is described by the formula:

x(t) = A sin(2pi*ft+θ)

where A is the amplitude of oscillation, f is the frequency, t is the elapsed time, and θ is the phase of the oscillation. The phase determines or is determined by the initial displacement at time t = 0. A motion with frequency f has period T = 1/f.


& an interval of space at a moment in time. Simple harmonic motion is a displacement that varies cyclically, as depicted to the right.