1. A spring mass system serving as a shock absorber under a car's suspension, supports the M=1000kg mass of the car. For this shock absorber, k=1000N/m and c=2000N s/m. The car drives over a corrugated road with force F=2000sin(wt)N . Use your notes to model the second order differential equation suited to this application. Simplify the equation with the coefficient of x'' as one. Solve x (the general solution) in terms of using the complimentary and particular solution method. In determining the coefficients of your particular solution, it will be required that you assume w2 -1=w or . Do not 1-w2=-w use Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w. You must indicate in your solution: 1. The simplified differential equation in terms of the displacement x you will be solving 2. The m equation and complimentary solution 3. The choice for the particular solution and the actual particular solution xp 4. Express the solution x as a piecewise function in terms of w
1. A spring mass system serving as a shock absorber under a car's suspension, supports the M=1000kg
mass of the car. For this shock absorber,
k=1000N/m and c=2000N s/m. The car drives over a corrugated road with force F=2000sin(wt)N
. Use your notes to model the second order differential equation suited to this
application. Simplify the equation with the coefficient of x'' as one. Solve x (the general solution) in
terms of using the complimentary and particular solution method. In determining the coefficients of
your particular solution, it will be required that you assume w2 -1=w or . Do not 1-w2=-w
use Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w.
You must indicate in your solution:
1. The simplified differential equation in terms of the displacement x you will be solving
2. The m equation and complimentary solution
3. The choice for the particular solution and the actual particular solution xp
4. Express the solution x as a piecewise function in terms of w
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