In: Physics
Consider a mass-spring-dashpot system with mass 5kg, a spring which is stretched 6 meters by a force of 20N, and a dashpot which provides 4N resistance for each m/s of velocity. The mass is also acted on by a periodic force 5 cos(ωt) for some number ω. For what value of ω (if any) does practical resonance occur? If the mass starts at rest, at equilibrium, find a formula for x(t) in terms of ω, the distance between the mass and the equilibrium point t seconds after motion starts.