This problem is an example of critically damped harmonic motion. A mass m = 8 is

Question

This problem is an example of critically damped harmonic motion.
A mass m=8 is attached to both a spring with spring constant k=72 and a dash-pot with damping constant c=48.

The ball is started in motion with initial position x0=2 and initial velocity  v0=?11 .

Determine the position function  x(t).

x(t)=                          

Graph the function x(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)=C0cos(?0t??0). Determine C0, ?0 and ?0.

C0=                          
?0=                          
?0=                          

Explanation / Answer

x(t)=(4-t)*e^(-4*t)

====================

x(t) = mx" + Cx' + kx=0
x(t) = mr" + Cr' + k=0
find r
and that would give you the r for its general differential equation
Find C_1 and C_2
do the Sqrt ((C_1)^2 + (C_2)^2) to find C1
omega1= the r
alpha 1 = arctan ((C_2)/(C_1))
forgot how to find p

second part
similar steps except use: x(t) = mx" + kx = 0

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.