1. Tardigrade
  2. Question
  3. Physics
  4. The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E1 and E2 are the total mechanical energies respectively. Then,

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_1 \, and \, E_2 $ are the total mechanical energies respectively. Then,Physics Question Image

Solution:

$E= \frac {1}{2}m \omega^2A^2 $
or $\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, E\propto A^2, $
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \frac {E_2}{E_1}= \bigg (\frac {A_2}{A_1}\bigg )^2= \bigg (\frac {a}{2a}\bigg )^2 $
or $\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, E_1=4E_2 $