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2. The differential equation for free motion of a spring-mass-damper system is: d?x dx + 2y +kx= 0 dt2 dt where k? = 45(N/m/kg), y = 0.5 s-1, x(0) = 0, = 0.2 m/s. %3D %3D %3D dt It=0 a) Solve the ODE over the interval 0 sts4 with Euler's explicit method using h = 0.5. b) Solve the ODE over the interval 0sts4 with midpoint method using h= 0.5. !! c) Plot the curve according to your solution for both (a) and (b).

2. The differential equation for free motion of a spring-mass-damper system is: d?x dx + 2y +kx= 0 dt2 dt where k? = 45(N/m/kg), y = 0.5 s-1, x(0) = 0, = 0.2 m/s. %3D %3D %3D dt It=0 a) Solve the ODE over the interval 0 sts4 with Euler's explicit method using h = 0.5. b) Solve the ODE over the interval 0sts4 with midpoint method using h= 0.5. !! c) Plot the curve according to your solution for both (a) and (b).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. The differentialequation 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-1, x(0) = 0, = 0.2 m/s. %3D %3D dt Ies0 a) Solve the ODE over the interval 0st<4 with Euler's explicit method using h = 0.5. b) Solve the ODE over the interval0sts4 with midpoint method using h=0.5. c) Plot the curve according to your solution for both (a) and (b).
Transcribed Image Text:2. The differentialequation 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-1, x(0) = 0, = 0.2 m/s. %3D %3D dt Ies0 a) Solve the ODE over the interval 0st<4 with Euler's explicit method using h = 0.5. b) Solve the ODE over the interval0sts4 with midpoint method using h=0.5. c) Plot the curve according to your solution for both (a) and (b).
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