A particle of mass m moves in a potential of the form V(x)= 2 cx² cx4 where c is a constant. Determine the range of energies for periodic motion, nonperiodic motion with change of direction, and nonperiodic motion without change of direction. What is the period of small oscillation?

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Q: U(x) = U, e-x/a A particle of mass m moves in the one-dimensional potential x2 U(x) = U,

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A: Required : Plot of the potential.

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Q: To be able to solve rectilinear problems with variable functions. A particle moves with harmonic…

A: The basic relation of Harmonic motion is, Displacement, X = Asinωt Velocity, X. = Aωcosωt…

Q: Sketch the phase portrait corresponding to the potential obtained in part (a).

A: Here, we plot the graph.

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Q: Mass is attached to a spring and set to oscillate horizontally on a frictionless surface.  At what…

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Q: 2-a) Using the matrix treatment derive the energy eigen values for the Hint: harmonic oscillator…

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Q: m The Lagrange's equation is given by 1 L ==ma²t² - mabtcos08 +mb²0² + mgbcose.

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Q: There is a particle of mass m in the following potential. x a How many useful modes are there? How?

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A: Given,  mass , m = 295.0 g = 0.295 kg spring constant , k = 13.44 N/m equilibrium position = 21.5 cm…

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Q: In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with particles or rigid…

A: ## The student has asked to answer 3.2 specifically!!

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A: using same concept both question can be answered. the conept is as follows:

Q: 3. Give a formula for the tangent of the l = 0 phase shift for scattering by a potential { for all E…

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Q: Find a scalar potential, fi, if  F=(3x^2yz^2)i+(x^3z^2)j+(2x^3yz)k, and fi(1,1,1)=1

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Q: U(x) Question 2: An object with a mass of 0.5kg and potential energy expressed as…

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Q: By using hamiltonian equations. Find the solution of harmonic oscillator in : A-2 Dimensions  B-3…

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Q: Write the elongation matrix.

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