A particle of mass $m$ moves in the potential energy $U$ shown above. The period of the motion when the particle has total energy $E$ is
Advanced
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1If a spring extends by $x$ on loading, then energy stored by the spring is (if $T$ is the tension in the spring and $K$ is the spring constant)View Solution
- 2Phase 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. $Image$View Solution
$1.$ The phase space diagram for a ball thrown vertically up from ground is
mcq $Image$
$2.$ The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_1$ and $E_2$ are the total mechanical energies respectively. Then $Image$
$(A)$ $ E_1=\sqrt{2} E_2$ $(B)$ $ E_1=2 E_2$
$(C)$ $ E_1=4 E_2$ $(D)$ $ E_1=16 E_2$
$3.$ 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 $Image$
mcq $Image$
Give the answer question $1,2$ and $3.$
- 3View SolutionA hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will
- 4View SolutionA tunnel has been dug through the centre of the earth and a ball is released in it. It will reach the other end of the tunnel after
- 5A body executes $SHM$ under the influence of one force and has a period $T_1\, second$ and the same body executes $SHM$ with period $T_2\, second$ when under the influence of another force. When bothforces act simultaneously and in the same direction, then the time period of the same body isView Solution
- 6Two simple harmonic motions are represented by the equationsView Solution
${x}_{1}=5 \sin \left(2 \pi {t}+\frac{\pi}{4}\right)$ and ${x}_{2}=5 \sqrt{2}(\sin 2 \pi {t}+\cos 2 \pi {t})$
The amplitude of second motion is ....... times the amplitude in first motion.
- 7For a particle executing $S.H.M.$ the displacement $x$ is given by $x = A\cos \omega t$. Identify the graph which represents the variation of potential energy $(P.E.)$ as a function of time $t$ and displacement $x$View Solution
- 8Two pendulums have time periods $T$ and $5T/4.$ They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum they will be again in the same phase :View Solution
- 9As per given figures, two springs of spring constants $K$ and $2\,K$ are connected to mass $m$. If the period of oscillation in figure $(a)$ is $3 s$, then the period of oscillation in figure $(b)$ will be $\sqrt{ x }$ s. The value of $x$ is$.........$View Solution
- 10A spring whose unstretched length is $\ell $ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $\ell_1$ and $\ell_2$ where, $\ell_1 = n\ell_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants, $k_1$ and $k_2$ will beView Solution