A loudspeaker cone of mass is held by a suspension whose restoring force per unit…

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Oscillations and normal modes · Oscillations and normal modes

Modes, Packets and Media, Ch The anharmonic oscillator: frequency, harmonics and drift

Problem

A loudspeaker cone of mass

m = 1.0\,\text{kg}

is held by a suspension whose restoring force per unit mass follows from the potential energy

V(x) = \tfrac12kx^2 + px^3

, with

k = 100\,\text{N m}^{-1}

and

p = -5.0\,\text{N m}^{-2}

x

the displacement of the cone from its rest position. There is no quartic term. ((a)) Write the equation of motion in the standard form

\ddot x + \omega_0^2x + \eta x^2 + \varepsilon x^3 = 0

. ((b)) Give numerical values of

\omega_0

\eta

and

\varepsilon