Timeline for Deriving the differential equation of simple harmonic motion through energy conservation equation
Current License: CC BY-SA 4.0
3 events
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| Oct 9 at 19:29 | comment | added | JEB | @User198 I know, that's why we didn't solve forces, nor did we find a stationary action or it's transform to a hamiltonian; rather, we balanced the power flowing between kinetic and potential energies. And we didn't use $H$, which is formally a Legendre transform of $L$. We used energy: $E=T+V$ and $dE/dt=0$ to get $dT/dt = - dV/dt$. Is that not different? | |
| Oct 9 at 16:46 | comment | added | User198 | Thanks, but this is not actually what I was interested in. I have no trouble in doing the steps of deriving the equation, but I was just wondering in how was I able to skip using the Lagrange or Hamilton's equations and get the answer only by using the $\frac{dH}{dt}=0$. | |
| Oct 9 at 16:05 | history | answered | JEB | CC BY-SA 4.0 |