Lesson 27.1 - Extra Practice Solving IVPs Containing Dirac Delta Functions

1. Solve the IVP: $y^{″}+2y^{\prime }-3y=\delta (t-1)-\delta (t-2)$; $y(0)=2$, $y^{\prime }(0)=-2$

2. Solve the IVP: $y^{″}+6y^{\prime }+5y=e^t\delta (t-2);$ $y(0)=0$, $y^{\prime }(0)=4$

3. A mass attached to a spring is released from rest $1$ m below equilibrium positions from the mass spring system and begins to vibrate. After $\pi$ seconds, the mass is struck by a hammer exerting an impulse on the mass. This is modeled by following the IVP:

Find $y(t)$ where $y(t)$ is the displacement of the mass at any time $t$.

Next Lesson: Lesson 28 - Solving Linear Systems with Laplace Transforms

Table of Contents: Table of Contents