Conisder the spring -mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is

Q. Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is

Q. Consider the spring-mass system, with the mass submerged in water as shown in the figure. If mass is released with spring at natural length, then momentum-position diagram for one cycle of this system is (take down direction negative) (given density of mass is more than density of water).

Q. As shown in the figure, a mass of 100 kg is held between two springs. The natural frequency of vibration of the system in cycle/s, is

Q. 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 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 position or momentum upwards (or to right) is positive and downwards (or to left) is negative.

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Q. The time period of the spring mass system as shown in figure will be