Find the steady-state response of a damped single-degree-of-freedom system subjected to a harmonic base motion, considered in Section 3.6, using Laplace transform.

Data From Laplace Tranform:-

Equation 3.25, 3.28 and 3.29:-

Data From Example 3.15

Figure 3.1:-

Transcribed Image Text:

Steady-State Response Using Laplace Transform Find the steady-state response of a damped single-degree-of-freedom system subjected to a har- monic force f(t) = Focos of using Laplace transform. Solution: The Laplace transform of Eq. (3.1) leads to the relation (with zero initial conditions for steady-state response in Eq. (E.1) of Example 3.15) F(s) X(s) m(s + 25ws + w) S The Laplace transform of the input f(t) = Fo cos of is given by F(s) = F032 + w becomes Fo S X(s) = k where the relations w and = m 2V mk ing the right-hand side of Eq. (E.2) as 1 (E.1) Thus Eq. (E.1) (E.2) m (s + w) (s + 25ws + w) have been used in expressing Eq. (E.2). By express- Fo as+a2 F(s) = + a3s+a4 + 25ws + w. 2 the constants a1, a2, a3, and a4 can be identified as (see Problem 3.110) a w - w (25wn) w + (ww) 25w,w (E.3) (E.4) a2 = (E.5) (25w) w + (ww)