This problem is an example of critically damped harmonic motion. A mass m - 4 kg is attached to both a spring with spring constant k = 144 N/m and a dash-pot with damping constant c = 48 N-s/m. The ball is started in motion with initial position = 3 m and initial velocity t = -20 m/s. Determine the position function r(t) in meters. Graph the function (t). Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Solve the resulting differential equation to find the position function (). In this case the position function u(t) can be written as u(t)- Cocos(walan). Determine Co. wo and a Co Wo (assume 0 << 2m ) Finally, graph both function z(t) and u(t) in the same window to illustrate the effect of damping. ap
This problem is an example of critically damped harmonic motion. A mass m - 4 kg is attached to both a spring with spring constant k = 144 N/m and a dash-pot with damping constant c = 48 N-s/m. The ball is started in motion with initial position = 3 m and initial velocity t = -20 m/s. Determine the position function r(t) in meters. Graph the function (t). Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Solve the resulting differential equation to find the position function (). In this case the position function u(t) can be written as u(t)- Cocos(walan). Determine Co. wo and a Co Wo (assume 0 << 2m ) Finally, graph both function z(t) and u(t) in the same window to illustrate the effect of damping. ap
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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Transcribed Image Text:This problem is an example of critically damped harmonic motion.
A mass m = 4 kg is attached to both a spring with spring constant k = 144 N/m and a dash-pot with damping constant
c = 48 N-s/m.
The ball is started in motion with initial position = 3 m and initial velocity = -20 m/s.
Determine the position function z(t) in meters.
z(t) =
Graph the function (t).
Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Solve
the resulting differential equation to find the position function ().
In this case the position function u(1) can be written as u(1) - Cocos (wlan). Determine Co. wo and an
5 3
Co-
والها
8
(assume 0 < a < 2π)
Finally, graph both function (t) and u(t) in the same window to illustrate the effect of damping.
11
ap
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