Discuss two applications of second-order linear differential equations.

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Aidyn Mccarthy · Accepted Answer

We can use second order differential equations for studying spring/mass systems, for example, the differential equation for free damped motion.

m \frac{d^{2} x}{d t^{2}} + \frac{β}{m} \frac{d x}{d t} + \frac{k}{m} x = 0

where r(t) denotes the position at instant t, m the mass,

β

is a positive damping constant and k is a proportion constant.
We can also use second order differential equations for LRC-series circuits.
The charge q(t) can be computed by solving the differential equation

L \frac{d^{2} q}{d t^{2}} + R \frac{d q}{d t} + \frac{1}{C} q = E (t)

where L denotes the inductance, R the resistance, C the capitance and E(t) the voltage impressed on the circuit.
Result:
Spring/mass systems and LRC-series circuits.

Discuss two applications of second-order linear differential equations.

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