Question

Choose and state a vehicle from the assigned class above. Next,
to construct your mathematical model, you may assume that the mass
of the vehicle is distributed evenly throughout the car (for
simplicity). Here, *m* (in kg) will represent the mass of
the vehicle, the dampener attached to the suspension will have a
damping coefficient of *c* (in N/(m/s)), and the spring
constant, otherwise known as the spring rate, of the coil in the
suspension application will be *k* (in N/m). Without an
external force acting on the suspension, the second order
differential equation governing this system is given below.

Mass is 1205 kg

*m/**4**y**''**+
c**y**'**+ky=0*

Enter in your value for the mass, converted into kg.

Spring constant for mini cooper S = 28.25 N/m

Write this second order differential equation as a first order matrix-vector system of differential equations. Show your work in detail.

Now, suppose the front left portion of your vehicle drifts off a curb of height 0.15 meters without an initial velocity. Write an appropriate initial condition using proper notation describing this event and pair it with your first order system.

Answer #1

A particular spring has a spring constant of 50 Newton/meters.
Suppose a 1/2 kg mass is hung on the spring and is initially sent
in motion with an upward velocity of 10 meters per second, 1/2
meter below the equilibrium position.
A) Write down the DE that models the motion of this spring.
B) Write down the initial conditions.
C) Find the equation of motion for the spring.
D) Suppose this spring mass system experiences a viscous damping
term that...

1) State the main difference between an ODE and a PDE?
2) Name two of the three archetypal PDEs?
3) Write the equation used to compute the Wronskian for two
differentiable
functions, y1 and y2.
4) What can you conclude about two differentiable functions, y1 and
y2, if their
Wronskian is nonzero?
5) (2 pts) If two functions, y1 and y2, solve a 2nd order DE, what
does the Principle of
Superposition guarantee?
6) (8 pts, 4 pts each) State...

do all five questions
Question 1
20 pts
Ignoring the effects of air resistance, if a ball falls freely
toward the ground, its total mechanical energy
Group of answer choices
increases
remains the same
not enough information
decreases
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Question 2
20 pts
A child jumps off a wall from an initial height of 16.4 m and lands
on a trampoline. Before the child springs back up into the air the
trampoline compresses 1.8 meters. The spring constant...

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