A mass m=4 is attached to both a spring with spring constant k=257 and a dashpot with damping constant c=4. The ball is started in motion with initial position x 0
​
=3 and initial velocity v 0
​
=8. Determine the position function x(t). x (t)
− Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form x(t)=C 1
​
e −pt
cos(ω 1
​
t−α 1
​
). Determine C 1
​
,ω 1
​
,α 1
​
and p. C 1
​
=
ω 1
​
=
α 1
​
=
p=
​
(assume 0≤α 1
​
<2π ) Graph the function x(t) together with the "amplitude envelope" curves x=−C 1
​
e −pt
and x=C 1
​
e −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)=C 0
​
cos(ω 0
​
t−α 0
​
). Determine C 0
​
,ω 0
​
and α 0
​
C 0
​
= ω 0
​
= α 0
​
= Finally, graph both function x(t) and u(t) in the same window to illustrate the effect of damping.