Example 4 – Plot the solution to Example 3 using the same values of y
used in the plot of Example 1, above. We now plot the function
In the range 0 < t < 20, and changing the vertical range to (-1,3), the graph
should look like this:
Again, there is a new component to the motion switched at t=3, namely, the
particular solution y
solution for t>3.
The Heaviside step function can be combined with a constant function and with
linear functions to generate square, triangular, and saw tooth finite pulses, as
Square pulse of size U
Triangular pulse with a maximum value Uo, increasing from a < t < b,
decreasing from b < t < c:
f(t) = U
Saw tooth pulse increasing to a maximum value Uo for a < t < b, dropping
suddenly down to zero at t = b:
Saw tooth pulse increasing suddenly to a maximum of Uo at t = a, then
decreasing linearly to zero for a < t < b:
y(t) = 0.5 cos t –0.25 sin t + (1+sin(t-3)) H(t-3).
(t) = [1+sin(t-3)] H(t-3), which changes the nature of the
in the interval a < t < b:
f(t) = Uo[H(t-a)-H(t-b)].
f(t) = U