Transcription of Second Order Differential Equations
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Second Order Differential Equations
3 Second Order Differential EquationsWe now turn to Second Order Differential Equations . Suchequations involve the Second derivative,y (x). Let s assume that we canwrite the equation asy (x) =F(x,y(x),y (x)).We would like to solve this equation using Simulink. This is accomplishedusing two integrators in Order to outputy (x)andy(x).input outputy y (b)input outputyy (a) outputyy input y (c) : Basic schemes for usingIntegrator blocks for solving secondorder Differential shown in (b), sendingy (x)into theIntegratorblock, weget outy (x). This is similar to usingy (x)to gety(x)in (a).
the simple harmonic oscillator model. Example 3.3. Damped Simple Harmonic Motion A simple modification of the harmonic oscillator is obtained by adding a damping term proportional to the velocity, x˙. This results in the differential equation mx¨ +bx˙ +kx …
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