Ejercicio Problem · Física I URV 2023

Problem (10 points). Damped oscillator and resonance

A particle of mass $m = 250\text{ g}$ undergoes damped harmonic motion with an oscillation frequency of $5\text{ Hz}$. It is observed that over an interval of $10\text{ s}$, the amplitude of the oscillations decreases by $30\%$.

a)

Determine the elastic spring constant $k$ and the damping parameter $b$. [4 points]

b)

Find the time required for the system's mechanical energy to drop to $10\%$ of its initial value. [3 points]

c)

If a sinusoidal driving force of amplitude $F_0 = 2\text{ N}$ is applied to the oscillator, can resonance in velocity take place? Can resonance in displacement (amplitude) occur? If so, compute the corresponding angular frequency of the driving force in each scenario. [3 points]