From the Lagrangian L(x,x)=-mx² 2 OA 1 mx2. ---kx²=0 2 2 Bmx-kx=0 ⒸCmx²+kx=0 Dmx²-kx²=0 12 kx2 find the Lagrange's equation of motion.
Q: A particle of mass m moving in one dimension is subject to the potential (x) = V₁²²2e-², a>0. a)…
A: We will first plot the graph of of given function qualitatively. Then we will do derivative test…
Q: which the Lagrangian is I = mc² (1-√√1-B²)-kx² where ß = == a) Obtain the Lagrange equation of…
A: Required to find the equation of motion.
Q: x²+x²y²kx²y² find the equation of motion: 2 2 xy=-2xy +kxy xy=-2xy +kxy For the Lagrangian L=…
A:
Q: The Lagrange polynomial that passes through the 3 data points is given by X;| -1.6| 2.5|7.7 Yi | 3.4…
A:
Q: 1. Consider the system with T = ² m(r² + r²ġ² + ż²) and U = A. B. C. D. mgz where z = cr²,8 = wt, by…
A: We have given a kinetic energy term and a potential energy term of the system then we can write…
Q: 8. The Lagrangian of a system is given as L = mx7+qAx,- qd, where the symbols have the usual…
A:
Q: From the Lagrangian L(x,x)=-mx². -kx2 find the Lagrange's equation of motion: 2 2 Amx²+kx=0 OB.mx2.…
A: To write the Euler Lagrange equation of Lagrangian given above
Q: i + e Find the open interval(s) on which the curve given by the vector-valued function is smooth.…
A: Given, r(t) = eti - e-tj + 2tk The differentiate of r(t) is r'(t) = d/dt {r(t)}
Q: The Hamiltonian of a certain system is given by [1 0 0 H = hw |0 0 0 Lo 0 1 Two other observables A…
A:
Q: 8.10** Two particles of equal masses m₁ = m₂ move on a frictionless horizontal surface in the…
A: The Lagrangian of the given system is,For m1=m2=m, the above equation can be written as follows:The…
Q: Find the norm of each of the following functions on the given interval and state the normalized…
A: we need to evaluate the integral of the square of the function over the interval, and then take the…
Q: m L = 1 {i² + (1+r)²a²} _K__ r ² 2 2 d L dt dr ƏL ər = mř − ma² (1 + r) + Kr = 0
A: We have to show, Lagrangian in blue is equals the answer in pink
Q: Obtain the value of the Lagrange multiplier for the particle above the bowl given by x^2+y^2=az
A: To find the Lagrange multiplier for the particle above the bowl defined by x2+y2=az, we need to set…
Q: Use the identity above to prove that Ã×(B×C) + B×(C×Ã)=Č×(B× Â).
A:
Q: Example 1: A particle is executing simple harmonic motion of period Tabout a centre O andit passes…
A: Let the time measured from A, then X=acos(muot)
Q: Problem 3: Cylinder on sliding plate A plate of mass Mp is attached to a spring (constant k). It can…
A:
Q: k20, y[0] - 1, у1] - 0
A: Given equation : yk+2-yk=0.5ukHere,k≥0, y0=1 and y1=0
Q: Set up the Lagrangian function for the mechanical system shown in Fig. , using the coordinates x1,…
A: We consider x1 and x2 as the generalised coordinates and then derive the potential and kinetic…
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: The Lagrangian for a one-dimensional harmonic oscillator is (a) kx 1 (b) mx2 (c) mx+ kx (d) mx + kx-
A: Here, we use the formula of Lagrangian to get the required.
Q: L=T-V = 1²2 8² +mg | Cos Write down the Lagrange equation for a single generalised coordinate q.…
A: We have a Lagrange given by L=T-V=ml2θ˙2/2+mglcosθ which is for the case of a simple pendulum of…
Q: Problem 4b. For a free particle H = show that if 2m qpt, P=p then {Q, P} is an integral of motion…
A: Given:For the free particle H = p22malso Q = 12mq2 -qpt and P = pTo prove:Q, P is a constant of…
Q: A cell of mass (M) moves to the top and is attached to a Corona virus of mass (m) by a neglected…
A: (1) There are two generalized coordinates in this system. The human cell is constrained to move in x…
Q: (1) Find the Lagrange function 2) Find the generalized forces of the constraint Qk (3) Find the…
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: Consider the curve described by the parametric equations x = t – 1, y = t? + 3t + 2. For which value…
A:
Q: 1) Determine the lagrange polynomial of second degree that can be used to approximate F(1.5) based…
A: Given: The data is as follows: Introduction: Lagrange polynomial is a technique to determine a…
Q: Consider the following Lagrangian describing the two-dimensional motion of a particle of mass m in…
A:
Q: Which of the following are Hermitian. (A) (B)-1 (C)-th (D) th d² Select correct choice: (a) A and C…
A:
Q: 3stm EpIforte For a particle moving under the action of conservative force, the Lagrangian of the…
A: Since we answer up to one question, we will answer the first question only. Please resubmit the…
Q: 40. (1-2)-¹
A:
Q: sinh z
A:
Q: Q2: 0 0 The Hamiltonian is represented by the matrix H = u 0 0 1 Where u is positive real number. 1…
A:
Q: Solve it?
A: L=12Mx2-12kx2The lagrangian equation of motionddt(δLδx)-δLδx=0δLδx=mxδLδx=kxmx+kx=0mx=-kxEquation of…
Q: Question Four: For the simple pendulum Shown: If the string is an elastic one with elastic (force…
A:
Q: Use the Euler's Lagrange equationto prove clearly that the shortest distance between two points in…
A:
Q: 39. Z z²+9
A:
Q: Consider a system with l = 1. Use a three-component basis, |m>, which are the simultaneous…
A: Solution: For l = 1, the allowed m values are 1, 0, -1 and the joint eigenstates are |1,1>,…
Q: The system shown in figure moves freely throughout the axis longitudinal (x3-X2)² a. Show the…
A: The lagrangian is given by Where L is the Lagrangian, T is the Kinetic energy of the system and V…
Q: By using hamiltonian equations. Find the solution of harmonic oscillator in : A-2 Dimensions B-3…
A: For a Harmonic oscillator, the Kinetic energy T and Potential Energy V are given by, Considering…
Q: = Consider the one-dimensional system whose Lagrange has the form: L(x; x) = f(xx). Let xo and xo Vo…
A: Given: L(x,x.)= f(xx.) As we know that the Lagrange's we have; ddt∂L∂x.+∂L∂x=0
Q: Using Lagrange's equation, obtain the equation of motion for a particle in plane polar coordinates.
A: A particle in a plane has a two-dimensional motion with two coordinates, x and y. Let the potential…
Q: show a specific vector (eigenvector) of the y-axis spin matrix. ħ 0 Sy ( (13) == 2 i
A:
Q: Use Lagrange's equations to find the equations of motion of a particle moving on a trajectory…
A: Required to find the equations of motion using Lagrange's equation.
Step by step
Solved in 2 steps with 2 images
- Answer the following question xy +x y(0) = 1 Q1:-Using Euler method to find y (2) using h=0.5 for y': Q2:-Using Rung-kutta method (R4) to find y (0.5) using h=0.5 for y' = -y In y ,y(0) = 0.5 Q3:- Find the integral (e** + x²) dx by Gaussian Quadrature. Q4:- Find * sin/x dx n=5 by trapezoidal and Simpson method.Please, I want to solve the question correctly, clearly and conciselyFind the differential of the function y=x2 +2x?
- . Obtain the Euler – Lagrange equation for the extremals of the functional X2 | [y2 - yy'+y'2 ]dlx X1Q. 4 Simple pendulum has a bob of mass m at hemong Suppert (pendulm wih maing Suppert) which mores on a horizortd line in Vertical plane in which the pendulum and the escillates Find Hhe Lagrangian Lagrange's equation ofI Motion. mi %3DConsider the schematic of the single pendulum. M The kinetic energy T and potential energy V may be written as: T = ²m²²8² V = -gml cos (0) аас dt 80 The Lagrangian L is given by L=T-V, and the Euler-Lagrange equations for the motion of the pendulum are given by the following second order differential equation in : ас 80 = 11 = 0 Write down the second order ODE using the specific T and V defined above. Please write this ODE in the form = f(0,0). Notice that this ODE is not linear! Now you may assume that l = m = g = 1 for the remainder of the problem. You may still suspend variables to get a system of two first order (nonlinear) ODEs by writing the ODE as: w = f(0,w) What are the fixed points of this system where all derivatives are zero? Write down the linearized equations in a neighborhood of each fixed point and determine the linear stability. You may formally linearize the nonlinear ODE or you may use a small angle approximation for sin(0); the two approaches are equivalent.
- d² Let  = Consider the orthonormal basis: dx² |1) = ₁(x) = [2) = ₂(x) = √sin(x) L 2π sin and (a) Find Â1) and Â12). The operator  can be expressed in a matrix form as follows:  = a₁1)(1| + a₁21)(2 + a21 2)(1| + a2212X<21. (b) Use part (a) to compute: amn= (m|Â\n); m, n = 1,2.College Physics Question