Laplace Transform for a Forced Harmonic Oscillator Equation \ Belief physics

Описание: #beliefphysics
#forcedharmonicosscillator
#laplace_transformations
#laplacetransforms
your searches
Differential Equations
Laplace transform for a forced harmonic oscillator equation
Write the equation and initial values
Apply the Laplace transform to both sides
linearity property
property about how the Laplace transform of a derivative is related to the Laplace transform of the original function
Derive the Laplace transform of sin(w*t)
Confirm with Laplace Transform
Partial fraction decomposition of L[x]
Decompose L[y] further by hand
"shifting on the s-axis" property.
Shifting on the s-axis property
finding the inverse Laplace transform
Write the final answer.
Why Laplace transforms are so useful
Differential equations
Studying the forced harmonic oscillator by taking a Laplace transform and studying its poles.

An equally valuable form of support is to simply share the videos.
It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.
links
   • Laplace transforms  
Laplace Transform
trapping region
partial fractions
shift on the s axis
forcing function
periodic solution
laplace transform second order differential equations
laplace transform examples
shifting on the s axis
poincare bendixson theorem
poincare bendixson theorem example
laplace transform completing the square
laplace transform of cos(wt)
laplace transform linear operator
inverse laplace transform
limit cycles in nonlinear systems
outward pointing normal vector