Ejercicio Exercise 1 - Damped oscillations · Física II URV 2024

a) Find the new angular frequency

Solución: $3.100$ rad/s / $\sqrt{9.6094}$ rad/s

a) Find the new period

Solución: $2.027$ s

a) Write the corresponding equation of motion

Solución: $x(t) = 0.0204 e^{-0.625 t} \cos(3.100 t + 2.943)$ m / $x(t) = -0.02 e^{-0.625 t} \cos(3.100 t)$ m

b) Sketch the total energy as a function of time

Solución: A smooth sketch showing total mechanical energy starting at $E_0 = 4.0 \times 10^{-4}\ \text{J}$ at $t = 0$ and monotonically decaying towards zero following an exponential envelope $E(t) = E_0 e^{-2\gamma t}$ without oscillating below zero.

b) Calculate the time elapsed until half of the initial energy is dissipated

Solución: $0.555$ s