This problem is an example of critically damped harmonic motion A mass m 7 kg is attached to both a spring with spring constant & 175 N/m and a dash-pot with damping constant e = 70 N-s/m The ball is started in motion with initial position zo6 m and initial velocity ty=-34 m/s Determine the position function ar(t) in meters. z(t)-6e^(-5t)-4te^(-5t) 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 c0) Solve the resulting differential equation to find the position function () In this case the position function su(t) can be written as u(t) Cocos(wit-ae). Determine Co. we and op C₂- wp-5 O (assume 0 ≤ 0 <2m)
This problem is an example of critically damped harmonic motion A mass m 7 kg is attached to both a spring with spring constant & 175 N/m and a dash-pot with damping constant e = 70 N-s/m The ball is started in motion with initial position zo6 m and initial velocity ty=-34 m/s Determine the position function ar(t) in meters. z(t)-6e^(-5t)-4te^(-5t) 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 c0) Solve the resulting differential equation to find the position function () In this case the position function su(t) can be written as u(t) Cocos(wit-ae). Determine Co. we and op C₂- wp-5 O (assume 0 ≤ 0 <2m)
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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i cant seem to find C0 and a0. My calculations led me to a0=-48.576 but this answer was marked as incorrect. please help!
Transcribed Image Text:This problem is an example of critically damped harmonic motion
A mass m= 7 kg is attached to both a spring with spring constant k = 175 N/m and a dash-pot with damping constant e 70 N-s/m
The ball is started in motion with initial position zo 6 m and initial velocity to -34 m/s.
Determine the position function z(t) in meters
z(t)= 6e^(-5t)-41e^(-5t)
Graph the function z(t)
Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (soc0). Solve the resulting differential equation to find the
position function ().
In this case the position function () can be written as u(t)- Cocos (wata). Determine Co. we and co
Co
W5
(assume 0 ≤ 0 <2m)
Finally, graph both function z(t) and u(t) in the same window to illustrate the effect of damping
Og
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