(1 pt) This problem is an example of critically damped harmonic motion. A mass m

Question

(1 pt) This problem is an example of critically damped harmonic motion.
A mass m=7 is attached to both a spring with spring constant k=567 and a dash-pot with damping constant c=126.

The ball is started in motion with initial position x0=9 and initial velocity v0=?83 .

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= (assume 0??0<2? )

Finally, graph both function x(t) and u(t) in the same window to illustrate the effect of damping.

Explanation / Answer

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.

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