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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
(please solve all parts for multiple thumbs up)
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3a48588-935d-41ad-9d27-f09e23e19c34%2Fe32481e2-b262-4149-bb50-2f0d97c3acf0%2F6w5xe2d_processed.jpeg&w=3840&q=75)
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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