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Professor Dave Explains
Linear Second-Order Differential Equations Part 1: Homogeneous Case
After a number of tutorials covering first-order differential equations, it's time to start tackling second-order differential equations. These contain a second derivative term, and they are quite useful in physics. To introduce these,...
Virtually Passed
2DOF Spring Mass System Proof
This is an alternate proof for finding the natural frequencies and natural modes for a 2 DOF system. This method can always be used, but it's easier to involve matrices for larger degrees of freedom.
The equation of motion...
The equation of motion...
Virtually Passed
under damped over damped critically damped vibration proof (part 1)
Here I prove the formulas for under damped over damped and critically damped motion of a spring mass dampener system
Professor Dave Explains
Finding Eigenvalues and Eigenvectors
Defining eigenvalues and eigenvectors, and outlining how to solve for them given a particular matrix.
Khan Academy
Khan Academy: Differential Equations: 2nd Order Linear Homogeneous Equations 4
Video shows using the foundation shown in previous videos how to more quickly find a solution to a second order linear homogeneous differential equation. Includes using initial conditions with the general solution to find a particular...
Khan Academy
Khan Academy: Differential Equations: Complex Roots of Characteristic Equation 1
Video is first part of showing what happens in a secondnd order linear homogeneous differential equation when the roots of the characteristic equation are complex. Includes using Euler's formula. [10:27]
Khan Academy
Khan Academy: Differential Equations: Complex Roots of Characteristic Equation 2
Video continues from previous video showing what happens when the roots of the characteristic equation are complex and deriving a formula for the general solution. Shows an example problem applying the formula derived to determine the...
Khan Academy
Khan Academy: Differential Equations: Repeated Roots of Characteristic Equations
Video shows what happens when the characteristic equation has repeated roots. Explains why just using the one root will not give a correct general equation. Shows an example of solving a differential equation where the characteristic...
Khan Academy
Khan Academy: Differential Equations: Complex Roots of Characteristic Equation 3
Video shows example of using formula derived in previous video for general solution of a differential equation when characteristic equation has complex roots. Includes using initial conditions to determine a particular solution. Shows...
Khan Academy
Khan Academy: Differential Equations:repeated Roots of Characteristic Equation 2
Video shows example of solving a second order linear homogeneous differential equation when the characteristic equation has repeated roots. Includes using initial conditions to find a particular solution. [8:52]