Delta Functions and Forcing

Impulse forcing like a hammer blow, modeled by the Dirac delta, and solving initial value problems driven by an input concentrated at one instant.

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6 exercises

Solve the initial problems in Solving Initial Value Problems using the Laplace transform, $\delta(t)$ is the unit impulse function.

$2 y'' + y' + 2y = \delta(t)$ , $y(0) = 0$ , $y'(0) = 0$

2.5

Solve the initial problems in Solving Initial Value Problems using the Laplace transform, $\delta(t)$ is the unit impulse function.

$y'' - y' - 2y = \delta(t - 5)$ , $y(0) = 0$ , $y'(0) = 0$

2.5

Solve the initial problems in Solving Initial Value Problems using the Laplace transform, $\delta(t)$ is the unit impulse function.

$\dfrac{d^2x}{dx^2} - 6 \dfrac{dx}{dt} + 25 x = \delta(t)$ , $x(0) = 1$ , $x'(0) = -2$

2.5

Solve the initial problems in Solving Initial Value Problems using the Laplace transform, $\delta(t)$ is the unit impulse function.

$y'' + 16y = \delta(t)$ , $y(0) = 1$ , $y'(0) = 0$

2.5

Solve the initial problems in Solving Initial Value Problems using the Laplace transform, $\delta(t)$ is the unit impulse function.

$y'' + 16y = \delta(t - 4)$ , $y(0) = 1$ , $y'(0) = 0$

2.5

Solve the initial problems in Solving Initial Value Problems using the Laplace transform, $\delta(t)$ is the unit impulse function.

$y'' + 2y' + y = \delta(t + 4)$ , $y(0) = -1$ , $y'(0) = 3$

2.5