Project #59337 - Differential Equations (Second Order and Laplace Transform)

I have three questions, I need someone to solve and explain the solution clearly. 

The first problem is second order DOE application, and the second and thrid are Laplace Transform problem and application. 

 


1. A car’s suspension system and springs and shock absorbers may be modeled as a spring-mass-dashpot system (see figure); irregularities in the road surface act as a forcing function. Suppose the mass of the car is 500 kg, the springs in the suspension system have constant 10^4 N/m, and the shock absorbers have damping coefficient 10^3 N/(m/sec). Suppose the road surface has periodic vertical displacement 0.5cos(pi/5 x) , where x is the position along the road.

(a) Show that y(t), the vertical displacement from the car’s equilibrium position, satisfies:

y''+2y'+20y=10cos(pi/5 vt), where v is the speed of the car.

2. Solve for inital probelm

x''+9x=4u(sub pi)(t) sin(t-pi), x(0)=0, x'(0)=1

3. the thrid problem you can see the file attached 

Subject Mathematics
Due By (Pacific Time) 02/26/2015 12:00 pm
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