Resonance (Example 9.4.2) unit:= (t,a,b) -> Heaviside(t-a) - Heaviside(t-b);

Zio2JUkidEc2IkkiYUdGJUkiYkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYtSSpIZWF2aXNpZGVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywmOSQiIiI5JSEiIkY0LUYtNiMsJkYzRjQ5JkY2RjZGJUYlRiU=

Square wave function F1 := t-> piecewise(0<t and t<=Pi, 10, Pi<t and t<=2*Pi,-10);

Zio2I0kidEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkqcGllY2V3aXNlRyUqcHJvdGVjdGVkRzYmMzIiIiE5JDFGMEkjUGlHRisiIzUzMkYyRjAxRjAsJEYyIiIjISM1RiVGJUYl

use Heaviside functions to get a few periods (at least for t>0, which is what we care for) F1per := t-> sum(Heaviside(t-2*Pi*n)*F1(t-2*Pi*n),n=0..5);

Zio2I0kidEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqJi1JKkhlYXZpc2lkZUdGKzYjLCY5JCIiIiomSSNQaUdGLEY1SSJuR0YlRjUhIiNGNS1JI0YxR0YlRjJGNS9GODsiIiEiIiZGJUYlRiU=

plot(F1per(t),t=0..6*Pi);

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

b1 := n-> (1/Pi)*int(F1(t)*sin(n*t),t=0..2*Pi);

Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiZJI1BpRyUqcHJvdGVjdGVkRyEiIi1JJGludEc2JEYrSShfc3lzbGliR0YlNiQqJi1JI0YxR0YlNiNJInRHRiUiIiItSSRzaW5HRi82IyomOSRGN0Y2RjdGNy9GNjsiIiEsJEYqIiIjRjdGJUYlRiU=

b1(n) assuming integer;

LCQqKEkjUGlHJSpwcm90ZWN0ZWRHISIiLCZGJiIiIilGJkkibkc2IkYoRihGKkYmISM/

Sawtooth wave function F2 := t-> 10*t * unit(t,-Pi,Pi);

Zio2I0kidEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqJjkkIiIiLUkldW5pdEdGJTYlRissJEkjUGlHJSpwcm90ZWN0ZWRHISIiRjFGLCIjNUYlRiVGJQ==

Use Heaviside functions to get a few periods F2per := t-> sum(Heaviside(t-(2*n+1)*Pi)*F2(t-(2*n+2)*Pi),n=-1..5);

Zio2I0kidEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqJi1JKkhlYXZpc2lkZUdGKzYjLCY5JCIiIiomLCZJIm5HRiUiIiNGNUY1RjVJI1BpR0YsRjUhIiJGNS1JI0YyR0YlNiMsJkY0RjUqJiwmRjhGOUY5RjVGNUY6RjVGO0Y1L0Y4O0Y7IiImRiVGJUYl

plot(F2per(t),t=0..6*Pi);

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

b2 := n-> (1/Pi)*int(F2(t)*sin(n*t),t=-Pi..Pi);

Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiZJI1BpRyUqcHJvdGVjdGVkRyEiIi1JJGludEc2JEYrSShfc3lzbGliR0YlNiQqJi1JI0YyR0YlNiNJInRHRiUiIiItSSRzaW5HRi82IyomOSRGN0Y2RjdGNy9GNjssJEYqRixGKkY3RiVGJUYl

b2(n) assuming integer;

LCQqJkkibkc2IiEiIilGJkYkIiIiISM/

Convolution solutions obtained using Laplace transform x1(t) := (1/8)*int(sin(4*(t-tau))*F1per(tau),tau=0..t): x2(t) := (1/8)*int(sin(4*(t-tau))*F2per(tau),tau=0..t): The displacement is periodic plot(x1(t),t=0..6*Pi,color=black);

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The amplitude of the displacement increases with time (linearly) we have resonance. plot(x2(t),t=0..6*Pi,color=black);

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