PROBLEM 24 - 0589: A forced oscillator is a system whose behavior can be described by a second-order linear differential equation of the form: ÿ + A¡ỷ + A2y (t) = (1) where A1, A2 are positive E(t) constants and E(t) is an external forcing input. An automobile suspension system, with the road as a vertical forcing input, is a forced oscillator, for example, as shown in Figure #1. Another example is an RLC circuit connected in series with an electromotive force generator E(t), as shown in Figure #2. Given the initial conditions y(0) = %3D Yo and y(0) = zo , write a %3D FORTRAN program that uses the modified Euler method to simulate this system from t = 0 to t = tf if: Case 1: E(t) = h where h is %3D constant Case 2: E(t) is a pulse of height h and width (t2 - t1). Case 3: E(t) is a sinusoid of amplitude A, period 2n/w and phase angle p . E(t) is a pulse train Case 4: with height h, width W, period pW and beginning at time t = t1.

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PROBLEM 24 - 0589:
A forced oscillator is a system
whose behavior can be
described by a second-order
linear differential equation of
the form:
ÿ + Ajý + A2y (t) =
(1)
where A1, A2 are positive
%3D
E(t)
constants and E(t) is an external
forcing input. An automobile
suspension system, with the
road as a vertical forcing input, is a
forced oscillator, for
example, as shown in Figure #1.
Another example is an RLC circuit
connected in series with
an electromotive force generator
E(t), as shown in Figure #2.
Given the initial conditions y(0) =
Yo and y(0) = zo , write a
%3D
FORTRAN program that uses the
modified Euler method to
simulate this system from t = 0 to t
= tf if:
Case 1:
E(t) = h whereh is
%3D
constant
Case 2:
E(t) is a pulse of
height h and width (t2 - t1) .
Case 3:
E(t) is a sinusoid of
amplitude A, period 2n/w
and phase angle p .
E(t) is a pulse train
Case 4:
with height h, width W,
period pW and
beginning at time t =
Transcribed Image Text:PROBLEM 24 - 0589: A forced oscillator is a system whose behavior can be described by a second-order linear differential equation of the form: ÿ + Ajý + A2y (t) = (1) where A1, A2 are positive %3D E(t) constants and E(t) is an external forcing input. An automobile suspension system, with the road as a vertical forcing input, is a forced oscillator, for example, as shown in Figure #1. Another example is an RLC circuit connected in series with an electromotive force generator E(t), as shown in Figure #2. Given the initial conditions y(0) = Yo and y(0) = zo , write a %3D FORTRAN program that uses the modified Euler method to simulate this system from t = 0 to t = tf if: Case 1: E(t) = h whereh is %3D constant Case 2: E(t) is a pulse of height h and width (t2 - t1) . Case 3: E(t) is a sinusoid of amplitude A, period 2n/w and phase angle p . E(t) is a pulse train Case 4: with height h, width W, period pW and beginning at time t =
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