Answer to Question #198551 in Classical Mechanics for TSHEPHISHO

Question #198551

a  harmonic oscillator has Hamiltonian, H=1/2 p^2+1/2 w^2 p^2 . Determine the Hamiltonian equation and the general solution


1
Expert's answer
2021-05-26T10:32:21-0400

H = p2/(2m) + ½kx2. H is a function of x and p, while the Lagrangian is a function of x and v.

Equations of motion: dx/dt = ∂H/∂p, dp/dt = -∂H/∂x.

dx/dt = p/m, dp/dt = -kx. We have two first-order differential equations which can be combined to yield the second order differential equation d2x/dt2 = -(k/m)x.

The coordinates and the Hamiltonian do not contain time explicitly, so H = E, and E = constant. The energy E is a conserved quantity.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS