A door-closer mechanism behaves as a mass on an effective spring of stiffness

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Simple, damped and driven oscillations · Simple, damped and driven oscillations

Mathematical Methods for Physics, Ch Second-order linear equations: damping, driving and resonance

Problem

A door-closer mechanism behaves as a mass

m = 0.50\,\mathrm{kg}

on an effective spring of stiffness

k = 8.0\,\mathrm{N\,m^{-1}}

, with a dashpot giving a resistive force proportional to speed with damping constant

b = 6.0\,\mathrm{kg\,s^{-1}}

. Its undriven closing motion obeys

\ddot{x} + \gamma\dot{x} + \omega_0^2 x = 0

. ((a)) Write down

\omega_0

and

\gamma

. ((b)) Solve the auxiliary equation for the two roots

\lambda

. ((c)) State which damping regime this is.

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