Ejercicio Lab 3 · Física II URV 2024

How does the action of the motor turn into a driving resonant force governing the motion of the mass?

Solución: The motor drives the upper support point (suspension point) of the spring in a periodic motion, $y_e(t) = Y_0 \cos(\omega t)$. As a result, the instantaneous elongation of the spring is $\Delta l(t) = y(t) - y_e(t)$, where $y(t)$ is the coordinate of the mass. The elastic force exerted on the mass becomes: $$F_e = -k[y(t) - y_e(t)] = -ky(t) + kY_0 \cos(\omega t)$$ Thus, the displacement of the suspension point creates an effective harmonic driving force $F_0 \cos(\omega t)$ with $F_0 = kY_0$ transmitted directly through the spring elasticity to the mass, driving it into forced oscillation and resonance when $\omega \approx \omega_0$.