The differential equation for free motion of a spring-mass-damper system is: dx dx dt2 + 2y+...

 

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The differential equation for free motion of a spring-mass-damper system is: d²x dx dt2 + 2y+ k²x = 0 dt where k? = 45(N/m/kg), y = 0.5 s, x(0) = 0, = 0.2 m/s. !3! %3D dt It=0 a) Solve the ODE over the interval 0 <t<4 with Euler's explicit method using h = 0.5. %3D b) Solvethe ODE over the interval 0stS4 with midpoint method using h=0.5. %3D c) Plot the curve according to your solution for both (a) and (b). The differential equation for free motion of a spring-mass-damper system is: d²x dx dt2 + 2y+ k²x = 0 dt where k? = 45(N/m/kg), y = 0.5 s, x(0) = 0, = 0.2 m/s. !3! %3D dt It=0 a) Solve the ODE over the interval 0 <t<4 with Euler's explicit method using h = 0.5. %3D b) Solvethe ODE over the interval 0stS4 with midpoint method using h=0.5. %3D c) Plot the curve according to your solution for both (a) and (b).

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