Consider the following. The downward direction.
Set up the spring-mass equation. (Use xp for x' and xpp for x''. Assume up is the positive direction)
Determine whether it is critically damped, under or overdamped.
The system is
Solve the IVP.
x(t)=
Consider the following: A 10 kg mass is suspended on a spring with spring constant k=20 N/m. The damping coefficient is b =30 kg/s. The mass is initially at equilibrium and is given an initial velocity of the downward direction. Set up the spring-mass equation. (Use xp for x and xpp for x. Assume up is the positive direction) 10xpp+30xp+20x=0 Determine whether it is critically damped, under or overdamped.
Solve the IVP.
X
x
1.5
0.5
0.5
1.0
8
10
12
6
8
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12
0.5
0.5
-0.5
6
8
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12
-1.0
-1.5
X
1.5
1.0
0.5
2
4
6
8
10
12
0.5