Question

Consider a particle moving in one dimension, with coordinate x and velocity ˙x. Suppose that the particle moves in a potential U(x) = 1/2 (kx^2) for constant k (a) Find the Lagrangian function L( ˙x, x). (b) Using the Euler-Lagrange equation, find the equation of motion for the coordinate x. (c) Solve the equation of motion of part (b) to find the trajectory x(t), for initial conditions x(0) = A, ˙x(0) = 0.

Name: consider a particle moving in one dimension with coordinate x and velocity x suppose that the particle moves in a potential ux 12 kx2 for constant k a find the lagrangian function l x x b using the eu
Uploaded: 2023-02-10T20:20:07-08:00
Duration: 1 min 54 s
Channel: Timothy James
Description: consider a particle moving in one dimension with coordinate x and velocity x suppose that the particle moves in a potential ux 12 kx2 for constant k a find the lagrangian function l x x b using the eu

          Consider a particle moving in one dimension, with coordinate x and velocity ˙x.
Suppose that the particle moves in a potential

U(x) = 1/2 (kx^2) for constant k

(a) Find the Lagrangian function L( ˙x, x).
(b) Using the Euler-Lagrange equation, find the equation of motion for
the coordinate x.
(c) Solve the equation of motion of part (b) to find the trajectory x(t),
for initial conditions x(0) = A, ˙x(0) = 0.

Added by Priyanka T.

Practice Problem in Physics for the JEE Main and Advanced

Abhay Kumar 2015 Edition

Chapter 3

Instant Answer

Solved by Expert Timothy James

02/10/2023

Step 1

First, find the Lagrangian function L( ˙x, x) using the Euler-Lagrange equation: L( ˙x, x) = -kx^2 + 1/2 (kx^2) Show more…

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Consider a particle moving in one dimension, with coordinate x and velocity ˙x. Suppose that the particle moves in a potential U(x) = 1/2 (kx^2) for constant k (a) Find the Lagrangian function L( ˙x, x). (b) Using the Euler-Lagrange equation, find the equation of motion for the coordinate x. (c) Solve the equation of motion of part (b) to find the trajectory x(t), for initial conditions x(0) = A, ˙x(0) = 0.