A mass m=4 is attached to both a spring with spring constantk=145 and a dash-pot with damping constant c=4.
The ball is started in motion with initial position x0=1and initial velocity v0=6 .
Determine the position function x(t) .
x(t)=?
Note that, in this problem, the motion of the spring isunderdamped, therefore the solution can be written in the formx(t)=c1e^(-Ït)cos(ω1t-α1) .Determine c1, ω1, Ï and α1.
c1=?
ω1=?
Ï=?
α1=?
Graph the function x(t) together with the \"amplitude envelope\"curves x=-c1e^(-Ït) and x=c1e^(-Ït).
Now assume the mass is set in motion with the same initial positionand velocity, but with the dashpot disconnected ( so c=0). Solvethe resulting differential equation to find the position functionu(t).
In this case the position function u(t) can be written asu(t)=c0cos(ω0t-α0). Determinec0, ω0,and α0.
c0=?
ω0=?
α0=?
