$A$ system exhibiting $S.H.M.$ must possess

Which of the following relationships between the acceleration $a$ and the displacement $x$ of a particle involve simple harmonic motion?
$(a)\; a=0.7 x$
$(b)\; a=-200 x^{2}$
$(c)\; a=-10 x$
$(d)\; a=100 x^{3}$

The equation of a simple harmonic motion is $X = 0.34 \cos(3000t + 0.74)$,where $X$ and $t$ are in $mm$ and $sec$ respectively. The frequency of the motion is:

The figure shows the circular motion of a particle. The radius of the circle is $B$. The particle starts at $t=0$ from the positive $y$-axis and moves clockwise. The simple harmonic motion of the $x$-projection of the radius vector of the rotating particle is given by:

Which of the following equations represents a simple harmonic motion? $(\omega$ is angular frequency, $A$ is amplitude of oscillation and $i = \sqrt{-1})$

The circular motion of a particle with constant speed is