HI1. A particle of unit mass moves along the positive x axis under a force:36f =x3x2a. Find the potential as a function of x; what is the equilibrium point? Sketch the force and the potentialand show that the motion is (i) oscillatory if E < 0 and (ii) unbounded for large x if E > 0.b. Given that E < 0 find the turning point (s) as a function of E.c. Find the period of the oscillatory motion.hint: You will need the following integral:dxV(x+ – x)(x – x_)it?(0)-to compute it, use the following substitution: x = x_ cos?(0) + x+ sin² (0) .d. Now expand the potential around the equilibrium, take the harmonic approximation (keeping up toquadratic terms near the minimum) and find the period in this approximation.e. Show that your results in c and d are consistent for small oscillations.

(Note: As the posted question has multiple subparts, according to the company policy, only the first…

Answered: A particle of unit mass moves along the…

Similar questions

3. Consider the gravitational force field F with G = m = M = 1 in 3D with the potential function being F(x, y, z) = 1 (√x² + y² + z²)³ 3 (—x, —y, —z). Show that the work done by the gravitational force as a particle moves from (x₁, y₁, 2₁) to (x2, Y2, 72) along any path depends only on the radii R₁ = √√x² + y² + z² and R₂ = x² + y² + z ².
I need the answer as soon as possible
Consider the one-dimensional potential U(x) = - Wd²(x² + d²) x4 + 8d4 Sketch the potential and discuss the motion at various values of x. Is the motion bounded or unbounded? Where are the equilibrium values? Are they stable or unstable? Find the turning points for E= -W/8. The value of Wis a positive constant.
The charge density on a disk of radius R = 11.2 cm is given by σ = ar, with a = 1.34 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 48.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. V R A
1.
3. Consider the vector field F F(x, y, z) = sin yi + x cos yî + – sin zk. (a) Show this vector field is conservative. (b) For this vector field, find a potential function o which satisfies (0, 0,0) = 2020.
Show that the vector field is conservative
A particle moves in a potential given by U(x) = -7 x3 + 2.1 x (J). Calculate the location of the stable equilibrium of this potential, in m. (Please answer to the fourth decimal place - i.e 14.3225)
3. Given the following scalar potentials (V), calculate the solution for the gradient of V (VV), and plot the vector arrow representation of this vector field over the given limits. (a) V = 15 + r cos o, for 0 < r < 10, and 0 < $ < 2n. (b) V = 100 + xy, for –10 < x < 10,
type only
Hello, can you help me with this problem please? Thank you
d and e

SEE MORE QUESTIONS

A particle of unit mass moves along the positive x axis under a force: 36 f = x3 9 x2 a. Find the potential as a function of x; what is the equilibrium point? Sketch the force and the potential and show that the motion is (i) oscillatory if E < 0 and (ii) unbounded for large x if E > 0.