Consider a one-dimensional potential $V(x)$ as shown in the figure below. A classical particle of mass $m$ moves under its influence and has total energy $E$ as shown below. The motion is
KVPY 2009, 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 simple pendulum oscillates with an amplitude of $50\, mm$ and time period of $2\, sec$, then its maximum velocity is .... $m/s$View Solution
- 2A $100 \,g$ mass stretches a particular spring by $9.8 \,cm$, when suspended vertically from it. ....... $g$ large a mass must be attached to the spring if the period of vibration is to be $6.28 \,s$.View Solution
- 3A particle executes simple harmonic motion with an amplitude of $4 \mathrm{~cm}$. At the mean position, velocity of the particle is $10 \mathrm{~cm} / \mathrm{s}$. The distance of the particle from the mean position when its speed becomes $5 \mathrm{~cm} / \mathrm{s}$ is $\sqrt{\alpha} \mathrm{cm}$, where $\alpha=$____________.View Solution
- 4In the figure given below. a block of mass $M =490\,g$ placed on a frictionless table is connected with two springs having same spring constant $\left( K =2 N m ^{-1}\right)$. If the block is horizontally displaced through ' $X$ 'm then the number of complete oscillations it will make in $14 \pi$ seconds will be $.........$View Solution
- 5A mass of $5\, {kg}$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4\, {m}$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed? (In ${m} / {s}^{2}$)View Solution
- 6When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude $a$ isView Solution
- 7The displacement of a particle from its mean position (in metre) is given by $y = 0.2\sin (10\pi t + 1.5\pi )\cos (10\pi t + 1.5\pi )$. The motion of particle isView Solution
- 8The velocity of a particle in simple harmonic motion at displacement $y$ from mean position isView Solution
- 9View SolutionIn damped oscillation graph between velocity and position will be
- 10A mass $M$ is suspended by two springs of force constants $K_1$ and $K_2$ respectively as shown in the diagram. The total elongation (stretch) of the two springs isView Solution
