Consider a spring-mass-damper system with mass \(=1.2 \mathrm{~kg}\) and damping ratio \(=0.05\), which is subjected to the periodic force shown in Figures P3.1a-c. Let the natural frequency of the system be \(\pi / T\).

a. Determine the steady-state response for each forcing function.

b. Verify your analytical results by numerical integration of the differential equations.

Figures P3.1(a, b, c)

Transcribed Image Text:

-T P f (t) Half sine wave 0 T 2T Figure P3.1a Periodic function with half sine waves f(t)^ P ADA -T T 2 -P T T 2 -P Figure P3.1b Periodic function with triangular waves f(t)^ P -2T -T 0 0.3T T 2T Figure P3.1c A periodic function with ramps