This problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both a spring with spring constant k = 200 N/m and a dash-pot with damping constant c= 80 N s/m. The ball is started in motion with initial position To = 9 m and initial velocity vo = Determine the position function z(t) in meters. I(t) 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 (so c= 0). Solve the resulting differentia equation to find the position function u(t). In this case the position function u(t) can be written as u(t)= Cocos (wotao). Determine Co, wo and co Co= Wo= ato = -48 m/s. (assume 0 ao < 2π) anh both function r(t) and u(t) in the same window to illustrate the effect of damping.

This problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both a spring with spring constant k = 200 N/m and a dash-pot with damping constant c= 80 N s/m. The ball is started in motion with initial position To = 9 m and initial velocity vo = Determine the position function z(t) in meters. I(t) 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 (so c= 0). Solve the resulting differentia equation to find the position function u(t). In this case the position function u(t) can be written as u(t)= Cocos (wotao). Determine Co, wo and co Co= Wo= ato = -48 m/s. (assume 0 ao < 2π) anh both function r(t) and u(t) in the same window to illustrate the effect of damping.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Problem 1.1MA

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

This problem is an example of critically damped harmonic motion.
A mass m = 8 kg is attached to both a spring with spring constant k = 200 N/m and a dash-pot with damping constant c= 80 N-s/m
The ball is started in motion with initial position to 9 m and initial velocity vo = -48 m/s.
Determine the position function z(t) in meters.
r(t) =
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 (so c = 0). Solve the resulting differential
equation to find the position function u(t).
In this case the position function u(t) can be written as u(t)= Cocos (wotao). Determine Co, wo and co
S 38 E
Co=
Wo=
(assume 0 do < 2π)
Finally, graph both function z(t) and u(t) in the same window to illustrate the effect of damping.
α0 =

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