If the spring-mass system has the equation of motion: d²x |dx|dx + a |dt| dt + kx = F, sin(wt) m dt2 Has a value of m = 2 kg , = 5N /(m/s)², and k = 6 N/m. The damping is nonlinear and represents damping from the air. The work function F0 sin(wt) has the values FO = 2.5 N and w = 0.5 rad/sec. Its initial condition when t = 0 s is the initial velocity dx(0)/dt = 0 m/s, and displacement initial x (0) = 1 m. So: a. Solve the above equation using Runge- Kutta order-4 with time period 0 sts 15 s and delta t = 0.5 s. %3D %3D %3D %3D (note: for this problem do a hand calculation from t = 0 – 5 s, the rest use excel)
If the spring-mass system has the equation of motion: d²x |dx|dx + a |dt| dt + kx = F, sin(wt) m dt2 Has a value of m = 2 kg , = 5N /(m/s)², and k = 6 N/m. The damping is nonlinear and represents damping from the air. The work function F0 sin(wt) has the values FO = 2.5 N and w = 0.5 rad/sec. Its initial condition when t = 0 s is the initial velocity dx(0)/dt = 0 m/s, and displacement initial x (0) = 1 m. So: a. Solve the above equation using Runge- Kutta order-4 with time period 0 sts 15 s and delta t = 0.5 s. %3D %3D %3D %3D (note: for this problem do a hand calculation from t = 0 – 5 s, the rest use excel)
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
![If the spring-mass system has the
equation of motion:
d²x
|dx|dx
+ a
|dt] dt
+ kx = F, sin(wt)
m
dt2
Has a value of m = 2 kg , = 5N /(m/s)², and
k = 6 N/m. The damping is nonlinear and
represents damping from the air. The
work function F0 sin(wt) has the values FO
= 2.5 N and w = 0.5 rad/sec. Its initial
condition when t = 0 s is the initial velocity
dx(0)/dt = 0 m/s, and displacement initial
x (0) = 1 m . So:
a. Solve the above equation using Runge-
Kutta order-4 with time period 0 sts
15 s and deltat = 0.5 s.
(note: for this problem do a hand
calculation from t = 0 – 5 s, the rest use
excel)
%3D
%3D
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4b1c269-29ab-4576-bf82-fe47f7f2bee3%2F4c06f6e2-4191-4e26-8083-e91c6ef079c8%2F4imco6a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If the spring-mass system has the
equation of motion:
d²x
|dx|dx
+ a
|dt] dt
+ kx = F, sin(wt)
m
dt2
Has a value of m = 2 kg , = 5N /(m/s)², and
k = 6 N/m. The damping is nonlinear and
represents damping from the air. The
work function F0 sin(wt) has the values FO
= 2.5 N and w = 0.5 rad/sec. Its initial
condition when t = 0 s is the initial velocity
dx(0)/dt = 0 m/s, and displacement initial
x (0) = 1 m . So:
a. Solve the above equation using Runge-
Kutta order-4 with time period 0 sts
15 s and deltat = 0.5 s.
(note: for this problem do a hand
calculation from t = 0 – 5 s, the rest use
excel)
%3D
%3D
%3D
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