Q 2: A mass m is suspended by a massless spring of spring constant k and unstretched length b. The suspension point has a constant upward acceleration a0. Gravity is acting vertically downward. Find the Lagrangian and Hamiltonian functions and obtain Hamilton’s equations of motion. What is the period of motion?

Q: A particle of mass m described by one generalized coordinate q moves under the influence of a…

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Q: please explain residual properties by cubic equations of state. for reading and understanding…

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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: Use Lagrangian formalism to solve the following problem: A block of mass m is held motionless on a…

A: Given data: mass of block=m, mass of plane=M, the angle of inclination=θ, a) change in vertical…

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

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

A: Reduced mass:

Q: H = ħwo 3 -i30 0 02 B = bo 7 | (0)) = i 1-i 1+i 1-i 6 D = (e₁] (0)) €₂(0)) (€3] (0)) 0 0 0 2a 2α 0…

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Q: The Lagrangian L = (x² + ÿ²) – mgy is defined a 2d projectile motion a) Please write Hamiltonian…

A: Since you have submitted a question with multiple subparts, we will solve the first 3 subparts for…

Q: Quantization of elastic waves. Let N particles of mass M be connected by a spring of force constant…

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Q: A freezer that is never turned off draws an average current of 2.4 A when it is plugged into a 115 V…

A: Electric Power is a rate of absorption of energy in the electrical circuit. Since this energy is…

Q: Verify that the Hamiltonian equation H(x, p, t) = T + V = p2/2m + (k/2) (x − v0t)2 leads to the same…

A: The Hamilton’s equations of motion are ∂H∂p=x˙, and ∂H∂x=-p˙ From Newton's second law p˙=mx¨

Q: Consider a free real scalar field $(x„), where r, = r, y, z for u = 1,2,3 and r4 = ict, satisfying…

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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: Determine the Lagrange Equation of Motion for the motion of a particle sliding down an inclined…

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Q: A particle of mass m oscillates in a vertical plane suspended by a massless string that goes through…

A: This is the problem with the simple pendulum with a variable length of the pendulum.  That is  of…

Q: For motion in a plane with the Hamiltonian H = |p|n − a r−n, where p is the vector of the momenta…

A: Given: The Hamiltonian of the motion in a plane is   The operator

Q: Consider the following Hamiltonian with constant m, n, and k, suppose that at t = 0 the system is at…

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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: The time-evolution of a physical system with one coordinate q is described by the La- grangian L = ?…

A: **as per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost…

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: Find the Hamiltonian and the equation of motion for a mass connected to a horizontal plane A with no…

A: To find the Hamiltonian and the equation of motion for a mass connected to a horizontal plane with…

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: The action of a system describes all of its possible trajectories in time, and it can be calculated…

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Q: The free space Lagrangian for a particle moving in 1D is L (x,x, t) = a) Show that pat = SL = ymv b)…

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

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Q: Problem 3.34. (a) Calculate the distribution PN (n) that n spins are up out of a total of N for N =…

A: Given data: p=q=12N=5, N=12

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

A: Given:  H = q2+p2

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

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Q: Q3: 0 1 The Hamiltonian is represented by the matrix H = B| 1 0 0 %3D 0 2 Where ß is positive real…

A: given: H=β010100002 Where, β is positive real number

Q: Find the equation of motion and the Hamiltonian corresponding to the Lagrangian L * = {{@, 9)² =…

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Q: Consider the motion of a point charge q in an electromagnetic field. Let E and B be the electric and…

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Q: Given the Hamiltonian H = p²/2m + a · p + V, with a = a(r) and V = the corresponding Lagrangian. If…

A: Here given that, Hamiltonian is H=p22m+a.p+V......................1Legrangian is the Logendre…

Q: (II) A particular race car can cover a quarter-mile track (402m) in 6.40s starting from a…

A: We have to determine the acceleration experienced by the driver, and the horizontal force exerted by…

Q: dx dy Consider the Lagrangian L= a| +b dt dt +cxy, where a,b and c are constants. If P, and p, are…

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Q: Q2. For a simple pendulum of length t, the angle Obetween rest position and deflected position is…

A: We are given kinetic energy T and potential energy V of the system.

Q: 3. A pendulum consist of a mass m suspended by a massless spring with natural length ro and spring…

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Q: 7-15. A pendulum consists of a mass m suspended by a massless spring with unextended length b and…

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Q: ** Problem 3.23 Consider the following Hermitian matrix: 2 i 1 T = -i 2 i 1 -i 2 (a) Calculate…

A: This problem can be solved using the properties of eigenvalues & eigenvectors. det(T) = product…

Q: Determine the equations describing ⟨x̂⟩and ⟨p̂⟩ for the Hamiltonian given by

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Q: Define a conservative system and state how the lagrange's equations are modified

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…