What is the projection of uniform circular motion?

The displacement equation of a particle is $x = 3\sin 2t + 4\cos 2t$. The amplitude and maximum velocity will be respectively:

$A$ particle free to move along the $x$-axis has potential energy given by $U(x) = k[1 - \exp(-x^2)]$ for $-\infty \le x \le +\infty$,where $k$ is a positive constant of appropriate dimensions. Then:

$A$ 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 $?$

The equation of the shown sinusoidal graph is

The distance covered by a particle undergoing $SHM$ in one time period is (amplitude $= A$).