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Lets say we have a mass connected to a spring.Assuming not any friction the ODE which describes the system is $m\frac{d^{2}x}{dt^{2}} = -kx$ We can set 2 Dirichlet boundary conditions $x(0)=0$ an...
#3: Post edited
by
Volpina
·
2023-06-08T19:15:11Z (over 1 year ago)
- Lets say we have a mass connected to a spring.Assuming not any friction the ODE which describes the system is
- $m\frac{d^{2}x}{dt^{2}} = -kx$
- We can set 2 Dirichlet boundary conditions $x(0)=0$ and $x(c)=0$ where $c$ will depend on $k,m$
If we solve the boundary condition problem we end up with a set of eigenvalues and eigenfunctions. Do the eigenfunctions and the eigenfunctions mean anything physically???
- Lets say we have a mass connected to a spring.Assuming not any friction the ODE which describes the system is
- $m\frac{d^{2}x}{dt^{2}} = -kx$
- We can set 2 Dirichlet boundary conditions $x(0)=0$ and $x(c)=0$ where $c$ will depend on $k,m$
- If we solve the boundary condition problem we end up with a set of eigenvalues and eigenfunctions. Do the eigenfunctions and eigenvalues have a physical meaning?
#2: Post edited
by
Volpina
·
2023-06-08T19:13:57Z (over 1 year ago)
- Lets say we have a mass connected to a spring.Assuming not any friction the ODE which describes the system is
- $m\frac{d^{2}x}{dt^{2}} = -kx$
- We can set 2 Dirichlet boundary conditions $x(0)=0$ and $x(c)=0$ where $c$ will depend on $k,m$
If we solve the boundary condition problem we end up with a set of eigenvalues and eigenfunction.Do the eigenfunctions and the eigenfunctions mean anything physically???
- Lets say we have a mass connected to a spring.Assuming not any friction the ODE which describes the system is
- $m\frac{d^{2}x}{dt^{2}} = -kx$
- We can set 2 Dirichlet boundary conditions $x(0)=0$ and $x(c)=0$ where $c$ will depend on $k,m$
- If we solve the boundary condition problem we end up with a set of eigenvalues and eigenfunctions. Do the eigenfunctions and the eigenfunctions mean anything physically???
#1: Initial revision
by
Volpina
·
2023-06-08T19:03:33Z (over 1 year ago)
What do eigenfunctions and eigenvalues mean physically?
Lets say we have a mass connected to a spring.Assuming not any friction the ODE which describes the system is
$m\frac{d^{2}x}{dt^{2}} = -kx$
We can set 2 Dirichlet boundary conditions $x(0)=0$ and $x(c)=0$ where $c$ will depend on $k,m$
If we solve the boundary condition problem we end up with a set of eigenvalues and eigenfunction.Do the eigenfunctions and the eigenfunctions mean anything physically???