MATH 251 Midterm: MATH 251 PSU s251HExam 2 mockup(sp09)
Document Summary
1: a 3 kg mass is suspended from a spring, which stretches the spring 5 m from its natural length. The system is placed into the liquid with damping constant 14 newton-seconds per meter. At t = 0, the system is at rest at its equilibrium position, then receives an external force of 6 cos( t) netwons. Assume is positive and g = 10m/s2. (a) set up an initial value problem that describes the motion of the mass. Be sure to explain any variables that appear in your equation. (b) for which value of will the system have resonance? (c) find the steady-state solution. From the equilibrium condition mg = kl, we have, Therefore, the equation of motion is given by, 3u + 14u + 6u = 6 cos t, u(0) = 0, u (0) = 0. Resonance occurs when the frequency is close to the natural frequency.
