A simple mass–spring system, subject to light damping, is vibrating under the action of a periodic force Fcos pt. The equation of motion is

where F and p are constants. Solve the differential equation for the displacement x(t). Show that one part of the solution tends to zero as t → ∞ and show that the amplitude of the steady state solution is

Hence show that resonance occurs when p = √2.

Transcribed Image Text:

dx dt +2- + 4x = Fcospt d.x dt