Equations $y_1 = A \sin \omega t$ and $y_2 = \frac{A}{2} \sin \omega t + \frac{A}{2} \cos \omega t$ represent $S.H.M.$ The ratio of the amplitudes of the two motions is

Which one of the following equations of motion represents simple harmonic motion? (Where $k, k_0, k_1$ and $a$ are all positive constants)

$A$ 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

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

If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \text{ m}$ represents the motion of a particle executing simple harmonic motion,the amplitude and time period of motion,respectively,are

Which of the following equations does not represent a simple harmonic motion?