For a damped harmonic oscillation, the equation of motion iswi

Question

For a damped harmonic oscillation, the equation of motion is

$m\tfrac{d^{2}x}{dt^{2}}+y\frac{dx}{dt}+kx=0$

with m = 0.25kg, y= 0.05kgs^-1and 70Nm^-1 Calculate (i) the period of motion, (ii) number of oscillations in which its amplitude will become half of its initial value, and (iii) the number of oscillations in which its mechanical energy will drop to half of its initial value.

22 Jan 2025

Answer :

Word Count : 135

We will solve the given damped harmonic oscillator equation numerically. The equation of motion is: \[ m \frac{d^{2}x}{dt^{2}} + y \frac{dx}{dt} + kx = 0 \] Given __________ _________ ______ ____ __________ _____ __________ ____ _______ ________ ____ ______.
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