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Open Loop Response of a car using a Basic First Order Model

  1. Jul 20, 2013 #1
    1. The problem statement, all variables and given/known data
    Car Dynamics

    f(t)→ [itex]\frac{\frac{1}{M}}{s+\frac{D}{M}}[/itex]→y(t)
    Applied Force Velocity

    2. Relevant equations
    M=1,000 kg and D=1000 kg/s
    Where f(t) represents the input force and y(t) is the output velocity. M is the Mass and D is the drag, both of which are assumed constant for each case to be considered.

    3. The attempt at a solution
    The first order Differential equation is y'(t)+[itex]\frac{D}{M}[/itex]y(t)=[itex]\frac{1}{M}[/itex]f(t)

    After I got that I'm supposed to do: I get stuck below at b part. I appreciate any help.

    b) Solve the differential equation for y(t) if the input is a step function scaled by the force F0, f(t)=F0u(t). The initial velocity y(0)=28.8m/s (75 km/hr). Choose F0 such that the final velocity is 100 km/hr (27.8 m/s).

    c) Plot the velocity y(t) versus time. Your time axis should go from 0 to 100 sec. Label axes.

    d) How does the velocity change if the drag, D, is reduced to 75 kg/s? Increased to 150 kg/s? Plot y(t) for both cases and compare to part b above.
     
    Last edited: Jul 20, 2013
  2. jcsd
  3. Jul 21, 2013 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    This problem has just been posed by elijah78 and addressed by the savants of PF.
     
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