Transcription of Second Order Differential Equations
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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). Asshown in (c), combining twoIntegratorblocks, we can inputy (x) =F(x,y,y )and get outyandy.
Hooke’s law, a stretched spring will react with a force F = kx, where x is the displacement of the spring from its unstretched equilibrium. The mass experiences a net for and will accelerate according to Newton’s Sec-ond Law of Motion, F = ma. Setting these forces equal and noting that a = x¨, we have mx¨ +kx = 0. m m k F = kx x
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