Page 488 - Dynamics of Mechanical Systems

0593_C13_fm Page 469 Monday, May 6, 2002 3:21 PM

Introduction to Vibrations 469

P13.2.12: A damped linear oscillator has a mass of 2 kg. Suppose the displacement x(t) of
the oscillator is given by:

+
xt () = e −15 . t ( Acos 4 t Bsin t 4 )
Determine the values of the damping c and spring stiffness k of the oscillator.
P13.2.13: See Problem P13.2.8. Find the solution to the following equations if x(0) = 1 and
˙ x (0) = –2.

a. 3˙˙ x + 2 ˙ x + 4x = 0
b. 4˙˙ xx++ 8x = 0
˙
c. 7 ˙˙ x − 4 ˙ x + 9x = 0

d. ˙˙ x + 5 ˙ x + 2 x = 0
e. 2˙˙ x + 4 ˙ x + 2x = 0

P13.2.14: Find the general solution of the following equations:

a. 3˙˙ x + 6x = 7cos 3t
b. 4˙˙ x + 7x = 8cos 4t
c. 2˙˙ x + 5x = 6sin 2t
d. 2˙˙ x + 5x = 6sin 2t + 7cos 3t

P13.2.15: See Problem P13.2.14. Find the solution to the following equations if x(0) = –1
and (0) = 2.
˙ x
a. 3˙˙ x + 6x = 7cos 3t
b. 3˙˙ x + 7x = 8cos 4t
c. 2˙˙ x + 5x = 6sin 2t
d. 2˙˙ x + 5x = 6sin 2t + 7cos 3t

P13.2.16: Find the general solution of the following equations:

a. 3˙˙ x + 2 ˙ x + 6x = 7cos 3t
b. 4˙˙ x + 3 ˙ x + 7x = 8cos 4t
c. 2˙˙ xx++ 5x = 6sin 2t
˙
d. 2˙˙ xx++ 5x = 6sin 2t + 7cos 3t
˙
P13.2.17: See Problem P13.2.16. Find the solution to the following equations if (0) = –1
˙ x
and x(0) = 2.
a. 3˙˙ x + 2 ˙ x + 6x = 7cos 3t
b. 4˙˙ x + 3 ˙ x + 7x = 8cos 4t
c. 2˙˙ xx++ 5x = 6sin 2t
˙
d. 2˙˙ xx++ 5x = 6sin 2t + 7cos 3t
˙