I've asked this question due a doubt in the following question.
The displacement of a particle along the $x$-axis is given by $x = a\sin^2\omega t$. The motion of the particle corresponds to
(1) simple harmonic motion of frequency $\omega/\pi$
(2) simple harmonic motion of frequency $3\omega/2\pi$
(3) non simple harmonic motion
(4) simple harmonic motion of frequency $\omega/2\pi$
According to various sources which I've referred the answer is contradictory.
(a) The answer given is option (3). This is is accordance to the following excerpt of the NCERT textbook.
$$\sin^2\omega t=\frac12-\frac12\cos2\omega t$$ The function is periodic having a period $T=\pi/\omega$. It also represents a harmonic motion with the point of equilibrium occuring at $\frac12$ instead of zero.
(b) But according to the book Concepts of Physics by HC Verma, and various others found on the internet, simple harmonic motion is defined as the one in which $F = -kx$ and sine function is one of its solutions.
If the equation is rearranged, as shown in the book, should it be considered as simple harmonic motion with equilibrium position at $+1/2$ unit and angular frequency of $2\omega$?
What is the exact difference between harmonic motion and simple harmonic motion?