A particle of mass m is forced to move on the inner surface of a smooth cone with side-peak angle α. Particle is under the influence of gravitational force. Find the serialized set of coordinates and obtain the bond equations. Find Lagrange's equations of motion. Note you can select cylindrical coordinates

Q: (b) Use Lagrange's equation to find the equation of motion of a head on a rigid parabolic wire with…

A: Let m denotes the bead’s mass, x and y denote coordinates of the bead at any time, U denotes the…

Q: Determine the Hamilton-Jacobi differential equation for the one dimensional motion of a particle of…

A: Given data, Potential of the particle :- V(x) = -bx

Q: mass m moves in a plane under the influence of a central force

A: According to the question, ody moves in the central force motion which depends only upon the…

Q: A particle of mass m is attracted to a center of force by a force of magnitude k/r2 , where k is a…

A:

Q: In terms of power, the hemispherical goblet of radius R can withstand the greatest perpendicular…

A: In polar coordinate system, the expression for kinetic energy will be, K.E(T)=12m.(r2.+r2θ2.) ,…

Q: 420 for a 2D 21 (;2 + 0 r² ) + Suppose that you have the Lagrangian L system in plane polar…

A: Lagrangian The Lagrangian of a system is a mathematical function that is a function of the…

Q: 2. 1D Ising model Consider the Ising model in 1D with zero external field. The Ising Hamiltonian in…

A: 1. Ground-state energy:The ground state of the 1D Ising model with zero external field has all spins…

Q: Q4: a) Calculate: (uz|A*|u6). b) If the Hamiltonian of harmonic oscillator defined as H = ħw + A*A…

A:

Q: The Hamiltonian of a three-level system is represented by the matrix Vo H = 2Vo + 2 \22 22 3Vo where…

A:

Q: Which of the following statements is false? I. The reduced mass of a two-particle system is always…

A: Reduced mass:

Q: q53 3x + x+ 1 Example 7.20. Using Lagrange's formula, express the function a sum of partial…

A:

Q: A particle in an attractive inverse-square force field k F = - (k is a positive constant) is…

A: Given: The particle is in the force field F=-kx2. Particle is projected along x-axis from the point…

Q: A particle of mass m slides from a height h on a smooth parabolic surface y = ax^2 Calculate the…

A: GIVEN Mass of the particle = m Particle slides from a height = h  parabolic surface y = ax^2…

Q: Q 4 For the motion of a projectile write the Lagrangian and the Hamiltonian functions in polar…

A: Let m is the mass of object, then kinetic energy in terms of rectangular coordinate will be,…

Q: (I) Define Lagrange's function for a conservative dynamical system of n particles. (II) If the…

A:

Q: A bead slides on the inner surface of a paraboloid z= C * r^4, as shown in Figure 2. C is a…

A:

Q: For the motion of a projectile write the Lagrangian and the Hamiltonian functions in polar…

A: The Lagrangian of a system is defined as:L=T-V………(1)where,T is the Kinetic energy.V is the Potential…

Q: Consider a block and a wedge. The block (mass m) has no friction when it moves on the wedge (mass M)…

A: Given: The mass of the block is m. The mass of the block is M. The angle of inclination is α.…

Q: A material point of mass m moves in space under the influence of an astral field forces, known…

A: A material point of mass m moves in space under the influence of an astral field forces, known…

Q: A particle of mass m is forced to move on the inner surface of a smooth cone with side-peak angle α.…

A:

Q: Consider a particle of mass m that is constrained to move on the surface of a cone of revolution z =…

A:

Q: Question 3 If the Lagrange's function for mechanical system is L = ;k (é² + g²(sin 0)² ) + g cos e.…

A: The Lagrangian is  L=12kθ˙2+12kϕ˙2sin2θ-gcosθ

Q: 17. Consider a particle in a one- dimensional simple harmonic oscillator, subject to perturbing…

A: Given x=h2mω(a+a+) where, h=h2π And from the rule of lowering and raising operator. a|n> =…

Q: A particle of mass m is subject to an attractive central force F(r) p3 For which values of the…

A: Given: A particle of mass m and attractive central force, Fr=-kr3

Q: Q. For a system with Hamiltonian H = q² + p², using Hamilton-Jacobi equation, find the Hamilton's…

A: Given:  H = q2+p2

Q: Problem 4: The center of a long frictionless rod is pivoted at the origin, and the rod is forced to…

A:

Q: Show that the Young's modulus Y, modulus of rigidity n and Poisson's ratio o are related by the…

A: In elasticity, Young's modulus=Modulus of rigidity=Poisson's ratio=

Q: Consider a large solar sail in the form of a square with sides of length e = 100 m that is…

A: Light is nothing but excitation of the electric and the magnetic field in space. It also behaves as…

Q: A particle of mass m is released from rest at a height y = h. (a) Write the Hamiltonian of the…

A:

Q: Consider the Lennard-Jones potential between atoms in a solid material. Find the dependence of the…

A: The Lennard-Jones potential is given by, V=4Eσx12-σx6 where E is the depth of the potential well or…

Q: Solve for y1(t) and y2(t) using Laplace Transforms and the initial values. You may check your work…

A:

Q: Consider a bead of mass m sliding down a wire from the point P (xo, yo). %3D 1. Write and expression…

A:

Q: If a particle of mass m is in a potential that is only a function of coordinates, calculate the…

A:

Q: 4. A particle of mass m moves in a central field of attractive force that has a magnitude () eat,…

A: Since given that Hamiltonian is time dependent then then energy is not conserved.

Q: Use the Euler's Lagrange equationto prove clearly that the shortest distance between two points in…

A:

Q: Consider an Atwood's machine consisting of 2 masses m1 and m2. The 2 masses connected by a…

A: For the atwoods machine Derive Lagrange equation Equation for conjugate momenta

Q: If the kinetic energy T and the potential energy V of a mathematical system are given T = (k+;) i +…

A: The Lagrangian function is given by, L = T - V The Hamiltonian function is given by, Hq, p, t =…

Q: A projectile is projected at an angle 0 degrees above a horizontal surface with a velocity v, from…

A: