# Applications of second order linear non homogenous ordinary differential equations

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

Delta2
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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.

Last edited:
• K Murty and member 587159