Phase space deagrams are useful tools  in analyzing all kinds of dynamical problems.
Channel: Doubtnut
Date: 2020-07-05

Phase space deagrams are useful toolsin analyzing all kinds of dynamical problems. They are especially usrful in studying the changes in motion as initial position and momenum are changed. Here we conseder 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 diagram is `x(t) vs. p(t) curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which positon or momentum upwards (or to right) is poitive and downwards (or to left) is negative.  Consider the spring-mass system, with mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is.