Welcome to Week 3 of
Differential Equations for Engineers. In this week, we'll learn about linear and
homogeneous differential equations. The second order ODE has
the form d squared x dt squared plus p of t dx,
dt plus q of t x equals g of t, where g of t is called
the inhomogeneous term. Inhomogeneous terms typically
represent forces that might be applied to an engineering system. We will focus on the inhomogeneous
second-order ODE with constant coefficients. Inhomogeneous terms, we will
consider our exponential functions, sine or cosine functions, and polynomials. We'll also learn about resonance and
damped resonance. Physically resonance occurs, when the frequency of the force matches
the natural frequency of the system. Mathematically resonance
happens when the inhomogeneous term is a solution of
the the homogeneous equation. Applications we'll learn about
are the resistor inductor capacitor or RLC circuit, a mass oscillating
on a spring, and a pendulum. Please join me in this third week of
Differential Equations for Engineers.