An earlier post looked at the effect of damping on free vibrations. We looked at the equation m u” + γ u’ + k u = 0 where the coefficients m, γ, and k were all positive. But what if…

This morning I ran across Pulp-o-mizer and decided my series of posts on mechanical vibrations could use a little sensational promotion. The posts are Part I: Introduction and free, undamped vibrations. Part II: Free, damped vibrations (under-damping, critical damping, over-damping)…

This is the final post in a four-part series on vibrating systems. The first three parts were free, undamped vibrations free, damped vibrations driven, undamped vibrations and now we consider driven, damped vibrations. We are looking at the equation m…

This is the third in a series of four blog posts on mechanical vibrations. The first two posts were Part I: Introduction and free undamped vibrations Part II: Free undamped vibrations

This is the second post in a series on vibrations determine by the equation m u” + γ u’ + k u = F cos ωt The first post in the series looked at the simplest case, γ = 0…

My favorite topic in an introductory differential equations course is mechanical and electrical vibrations. I enjoyed learning about it as a student and I enjoyed teaching it later. (Or more accurately, I enjoyed being exposed to it as a student…

What we call “differential equations” are usually not just differential equations. They also have associated initial conditions or boundary conditions. With ordinary differential equations (ODEs), the initial conditions are often an afterthought. First you find a full set of solutions,…

I studied nonlinear PDEs in grad school. My advisor, Ralph Showalter, would remind us occasionally what ‘nonlinear’ means. “Nonlinear” is not a hypothesis but the lack of a hypothesis. He meant a couple things by this. First, when people say…