The $$x$$-$$t$$ graph of a particle undergoing simple harmonic motion is shown in the figure. The acceleration of the particle at $$t=4/3$$ s is

Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

	Column I		Column II
(A)	Potential energy of a simple pendulum (y-axis) as a function of displacement (x) axis	(P)
(B)	Displacement (y-axis) as a function of time (x-axis) for a one dimensional motion at zero or constant acceleration when the body is moving along the positive x-direction	(Q)
(C)	Range of a projectile (y-axis) as a function of its velocity (x-axis) when projected at a fixed angle	(R)
(D)	The square of the time period (y-axis) of a simple pendulum as a function of its length (x-axis)	(S)

A simple pendulum has time period T₁. The point of suspension is now moved upward according to the relation y = Kt², (K = 1 m/s²) where y is the vertical displacement. The time period now become T₂. The ratio of $${{T_1^2} \over {T_2^2}}$$ is (g = 10 m/s²)

A small body attached to one end of a vertically hanging spring is performing SHM about its mean position with angular frequency $$\omega$$ and amplitude $$a$$. If at a height $$y^{\prime}$$ from the mean position, the body gets detached from the spring, calculate the value of $$y^{\prime}$$ so that the height $$\mathrm{H}$$ attained by the mass is maximum. The body does not interact with the spring during its subsequent motion after detachment $$\left(a \omega^{2}>g\right)$$