A mass m = 4 kg is attached to both a spring with spring constant k = constant c = 4 N s/m. The mass is started in motion with initial position o 3 m and initial velocity = 5 m/s. Determine the position function z(t) in meters. r(t) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form r(t) = Ciecos (wit - a). Determine C₁, w₁,ajand p. C₁ W₁ == aj = (e^(-1/2t))[((-5/6) sin(12t))+(3cos (12t))] Co Graph the function z(t) together with the "amplitude envelope" curves z=-C₁e- and z = C₁e. 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 (wot-ao). Determine Co. wo and a. والا (assume 0 ≤ a <2m)
A mass m = 4 kg is attached to both a spring with spring constant k = constant c = 4 N s/m. The mass is started in motion with initial position o 3 m and initial velocity = 5 m/s. Determine the position function z(t) in meters. r(t) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form r(t) = Ciecos (wit - a). Determine C₁, w₁,ajand p. C₁ W₁ == aj = (e^(-1/2t))[((-5/6) sin(12t))+(3cos (12t))] Co Graph the function z(t) together with the "amplitude envelope" curves z=-C₁e- and z = C₁e. 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 (wot-ao). Determine Co. wo and a. والا (assume 0 ≤ a <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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A mass m = 4 kg is attached to both a spring with spring constant k 577 N/m and a dash-pot with damping
constant c = 4 N. s/m.
The mass is started in motion with initial position o 3 m and initial velocity = 5 m/s.
Determine the position function z(t) in meters.
x(t)
Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form
r(t) Ciecos (wit-a₁). Determine C₁, w₁,ajand p.
C₁
WI
XX1
P
=
11
Co
(e^(-1/2t))[((-5/6)sin(12t))+(3cos(12t))]
Graph the function z(t) together with the "amplitude envelope" curves z-C₁e- and = ₁e pt.
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. we and co.
= ولما
(assume 0 ≤ a <2m)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88b5a342-0249-4890-b310-73ebb7656736%2Fbca8613a-da93-4d9b-92db-d59119e8cb3a%2F1vl8wxf_processed.png&w=3840&q=75)
Transcribed Image Text:=
A mass m = 4 kg is attached to both a spring with spring constant k 577 N/m and a dash-pot with damping
constant c = 4 N. s/m.
The mass is started in motion with initial position o 3 m and initial velocity = 5 m/s.
Determine the position function z(t) in meters.
x(t)
Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form
r(t) Ciecos (wit-a₁). Determine C₁, w₁,ajand p.
C₁
WI
XX1
P
=
11
Co
(e^(-1/2t))[((-5/6)sin(12t))+(3cos(12t))]
Graph the function z(t) together with the "amplitude envelope" curves z-C₁e- and = ₁e pt.
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. we and co.
= ولما
(assume 0 ≤ a <2m)
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