Which of the following is a necessary and sufficient condition for $S.H.M.$?

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

$A$ particle of mass $4 \text{ mg}$ is executing simple harmonic motion along the $x$-axis with an angular frequency of $40 \text{ rad s}^{-1}$. If the potential energy of the particle is $V(x) = a + bx^2$, where $V(x)$ is in joule and $x$ is in metre, then the value of $b$ is

$A$ 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 $?$

$A$ particle of mass $0.1 \ kg$ is executing simple harmonic motion of amplitude $0.1 \ m$. When the particle passes through the mean position,its kinetic energy is $8 \times 10^{-3} \ J$. If the initial phase is $45^{\circ}$,the equation of its motion is (Assume $x(t)$ as the position of the particle at time $t$)

$A$ particle is executing simple harmonic motion with an instantaneous displacement $x = A \sin^2(\omega t - \frac{\pi}{4})$. The time period of oscillation of the particle is