Paragraph: Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space

Step-by-step solution

Momentum is first positive but decreasing. Displacement (or say position). is initially zero. It will first increase. At highest point, momentum is zero and displacement is maximum. After that momentum is downwards (negative) and increasing but displacement is decreasing. Only (d) option satisfies these conditions. Analysis of Question (i) Question is simple. (ii) Since all the graphs given in question are parabolic type, we need not to check the mathematical part of the question.