What is the difference between periodic motion and simple harmonic motion?

$A$ particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small,which graph correctly depicts the position of the particle as a function of time $?$

Show that simple harmonic motion may be regarded as the projection of uniform circular motion along a diameter of the circle.

If the displacement of a particle is given by $x = 3 \sin (5\pi t) + 4 \cos (5\pi t) \text{ cm}$,what is the amplitude of the particle?

$A$ particle moves such that its acceleration $a$ is given by $a = -bx$,where $x$ is the displacement from the equilibrium position and $b$ is a constant. The period of oscillation is

The differential equation of a simple harmonic motion is given by $\frac{d^2y}{dt^2} + ky = 0$. What is the time period?