The differential equation describing the response of the diesel track suspension

Diesel Track Suspension System



1 Part 1: Diesel Track Suspension System
1.1 Differential Equation
The differential equation describing the response of the diesel track suspension
system under forced excitation is given as:
d2 x dx
m 2
+c + kx = F0 sin(2πf t)
dt dt
where:
• m is the mass of the system (given as 100 kg).
• c is the damping coefficient (given as 200 Ns/m).
• k is the spring linear stiffness (given as 10 kN/m).
• F0 is the amplitude of the harmonic force (given as 10 kN).
• f is the frequency of the harmonic force (given as 4 Hz).

1.2 Initial Conditions
The initial conditions are:
x(0) = X0 (where X0 is the last digit of your student number)
dx
(0) = n
dt

1.3 Solution
The solution of the differential equation is given by:
x(t) = 1.2767 sin(9.95t)+8.0176 cos(9.95t)+117.76 sin(25.13t)+11.13 cos(25.13t)

1.4 Numerical Differentiation
d2 x
To calculate dt2 from the obtained x(t) solution, we use numerical differentia-
tion:
d2 x x(t + ∆t) − 2x(t) + x(t − ∆t)
≈
dt2 (∆t)2

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