Question

The Lagrangian for a harmonic oscillator in the\ dimensionless form is $L(x, dot{x}) = frac{1}{2}dot{x}^2 - frac{1}{2}omega^2 x^2$.\ Find a solution of Euler-Lagrange equations\ which satisfies the following conditions:\ $x(t = 0) = 0$, $x(t = T) = X$, where $omega T < pi / 2$.\ Calculate the value of the action $S = int_0^T L(x(t), dot{x}(t))dt$\ for this path if $omega = 0.3$, $T = 1.9$ and $X = 4.2$

Name: The Lagrangian for a harmonic oscillator in thedimensionless form is L(x, dotx) = frac12dotx^2 - frac12omega^2 x^2.Find a solution of Euler-Lagrange equationswhich satisfies the following conditions:x(t = 0) = 0, x(t = T) = X, where omega T < pi / 2.Calculate the value of the action S = int0^T L(x(t), dotx(t))dtfor this path if omega = 0.3, T = 1.9 and X = 4.2
Uploaded: 2022-03-18T14:02:09-08:00
Duration: 6 min
Channel: Deepanshu Kumar
Description: The Lagrangian for a harmonic oscillator in thedimensionless form is L(x, dotx) = frac12dotx^2 - frac12omega^2 x^2.Find a solution of Euler-Lagrange equationswhich satisfies the following conditions:x(t = 0) = 0, x(t = T) = X, where omega T < pi / 2.Calculate the value of the action S = int0^T L(x(t), dotx(t))dtfor this path if omega = 0.3, T = 1.9 and X = 4.2

          The Lagrangian for a harmonic oscillator in the\
dimensionless form is $L(x, dot{x}) = frac{1}{2}dot{x}^2 - frac{1}{2}omega^2 x^2$.\
Find a solution of Euler-Lagrange equations\
which satisfies the following conditions:\
$x(t = 0) = 0$, $x(t = T) = X$, where $omega T < pi / 2$.\
Calculate the value of the action $S = int_0^T L(x(t), dot{x}(t))dt$\
for this path if $omega = 0.3$, $T = 1.9$ and $X = 4.2$

$The Lagrangian for a harmonic oscillator in thedimensionless form is L(x, dotx) = frac12dotx^2 - frac12omega^2 x^2.Find a solution of Euler-Lagrange equationswhich satisfies the following conditions:x(t = 0) = 0, x(t = T) = X, where omega T < pi / 2.Calculate the value of the action S = int0^T L(x(t), dotx(t))dtfor this path if omega = 0.3, T = 1.9 and X = 4.2$

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