Restoring and frictional forces of magnitudes kx and , respective

Question

Restoring and frictional forces of magnitudes kx and $\gamma \frac{dx}{dt}$ , respectively act simultaneously on an object of mass $0.2\text{ kg}$ attached to a spring. Under the influence of these forces, the mass oscillates with a frequency $1.5\text{ Hz}$ and its amplitude reduces to half in $4.0\text{ s}$ . Calculate the damping constant $\gamma$ , the force constant k and the damping factor b. Also write the differential equation for the system.

19 Jan 2026

Answer :

Word Count : 309

The motion of a damped harmonic oscillator is governed by the differential equation: [ m \frac{d^2 x}{dt^2} + \gamma \frac{dx}{dt} + k x = 0 ] where (m = 0.2 , \text{kg}), (\gamma) is the damping constant, and (k) is the spring constant. The damped frequency (f_d = 1.5 , \text{Hz}), so the angular frequency of damped oscillation is: [ \omega_d = 2 \pi f_d = 2 \pi \cdot 1.5 = 9.42 , \text{rad/s} ] Amplitude reduces ________ _______ _________ ____ __________ ______ _____ ________ ___.
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