1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

12.3 • VIBRATIONS IN MECHANICAL SYSTEMS 535

-------~EXERCISES FOR SECTION 12.3

For t hese exercises, use the results of Section 12.1.

1. Find the general solut ion to U" (t) + 3U' (t) + U (t) = F (t).

(a) F(t) = ~·

00 ( 1 )"+!

(b) F(t)= .. ~

1

~n-l cos((2n- l)t].

(c) F(t) is shown in F igure 12.20.

{

7f - t,

F(t)= t ,

• 'lf - t

for ~ $ t $ n;

for - 2 ~ $ t $ ~;

for -n<t< - 2 ...

Hint: F(t) = ~ E <:-^1 l; 2 sin[(2j- l)t].

7f j s l {2J - 1)

s

s = F(t)

Figure 12.20

2. Find the general solution to 2U" (t ) + 2U' (t) + U (t) = F (t).
   t

3. F(t) =

2

.

00 1

4. F(t)= z::-

2

-sin[(2n- l)t].

n = l n - 1

5. F (t) is shown in F igure 12.21.

s

1t

Figure 12.2 1