lct8 SDOF damped, general time-dependent load

Give can. form, general and homogeneous solution (recap)

First step for finging solution to particular solution

Get this? Single pulse

Get this? Series of pulses

Get this? Duhamel’s integral for viscously damped SDOF

Full genereal solution

Initial value problem

A: contribution of dulhamel’s integral starts after t;0, before t;0 it has no contribution

C: before t = 0 the duhamel’s integral has no influence on u(t)

Yes, init conditions = 0, and after t;0 equilibrium shifts, after delta_t it is back at 0.

Homogeneous sol: not needed, init cond. is zero. Free vibr is in the dulhamel’s integral.

SS response is a response to the force if t > infinity. F = 0 if t > infinity so no u;ss response.

U decreases over time in interval 0 < t < delta_t due to damping. so u(t) never reaches 0 after delta_t.