• ## Differential geometry of planar curves

In this blog we explore some basic concepts of the geometry of smooth curves in the plane. A moving point $$p$$ is described mathematically by letting $$p$$ be a function of time $$t$$, so that we can write $p(t)=(x(t),y(t)).$ The velocity is the first derivative of $$p$$ with respect to $$t$$, that is $v(t)=\frac{dp}{dt}(t)=\left(\frac{dx}{dt}(t),\frac{dy}{dt}(t)\right),$ For […]

• ## The damped and forced oscillator

We show how to solve the differential equation for mass on a spring with damping forces and a external periodic force acting on the mass.