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[w] in the equation a = -w^2.x indicates the [angular frequency] of the harmonic oscillator. The [angular frequency] is related to the [linear frequency] by the equation: w = 2.pi.f, where f is the linear frequency and pi is the mathematical constant 3.14159 .....
The general equation describing an harmonic oscillator can be written as,
x = A.sin(wt+p)
where A is the amplitude of oscillation, w is the angular frequency, t is the time, and p is the phase angle
The velocity v = dx/dt = w.A.cos(wt+p)
and acceleration a = dv/dt = -w^2.[Asin(wt+p)] = -w^2.x
[Be aware not to mix the angular frequency of a simple pendulum with the angular velocity of the pendulum. They are different physical quantities. The angular frequency of a simple harmonic oscillator, e.g. a simple pendulum, is a constant, but the angular velocity of the pendulum varies with the position (or time) of the pendulum.
In fact, the angular velocity of a simple pendulum is
= v/L = (w.A/L).cos(wt+p)
where L is the length of the pendulum
The max angular velocity = w.A/L
You can see from the equation that the angular velocity varies with time of oscillation, but the angular frequency is not.]
