Solution:Second Order Linear Non-Homogenous ODEs in Physics

[Dimitris Papadim]

Hello, could someone please give me some examples of where order linear non homogenous ordinary differential equations are used in physics[emoji4]

 

[Delta2]

They have many applications in almost all areas of physics.

For example in physics-electric circuits the differential equation that governs the behaviour of a RLC circuit with a resistor of ohmic resistance R, Capacitor of capacitance C and inductor of inductance L, all in series, which is driven by a voltage source V(t) is given by $\frac{q}{C}+R\frac{dq}{dt}+L\frac{d^2q}{dt^2}=V(t)$. q(t) is the charge of the capacitor C at time t.

Another example in physics-mechanics, the damped harmonic oscillator with mass m, spring constant k, and damping coefficient c, that is driven by an external force F(t) follows the 2nd order linear ordinary differential equation:
$m\frac{d^2x}{dt^2}+c\frac{dx}{dt}+kx=F(t)$. x(t) is the displacement of mass m at time t.