Page 137 - Dynamics of Mechanical Systems

0593_C04*_fm Page 118 Monday, May 6, 2002 2:06 PM

118 Dynamics of Mechanical Systems

and let the acceleration of O in R be:

RO 2
a =−6 n − 8 n + 2 n m sec
z
y
x
R Q
R P/Q
R P
Find: (a) a , (b) a , and (c) a . Check the results of (c) by evaluating where, as before,
r locates P relative to Q.
P4.9.3: A rod pendulum has a movable support as represented in Figure P4.9.3. Let the
pendulum length be 3 ft and let the horizontal displacement x of the support O and the
angular displacement θ of the rod be:
(
x = 2sin π t ) 4 ft
and

θ = π 3cos π ( ) 6 t

n
y
n
C x
O n r
x y φ n z
O
θ n
x n
G θ θ
n θ
G
n z
P n
n
P
FIGURE P4.9.3 FIGURE P4.9.4
A rod pendulum with a horizontally moving A rod pendulum with a support moving vertically
support. on a circle.

Find the velocity and acceleration of the rod center G and the rod extremity P for time
t equal to (a) 0, (b) 1, and (c) 2 sec. Express the results in terms of the unit vectors sets n ,
x
n , n and n , n , n , as shown in Figure 4.9.4.
θ
z
z
y
P4.9.4: See Problem 4.9.3. Instead of moving on a horizontal line, let the pendulum support
O move on a vertical circle as in Figure P4.9.4. As before, let the pendulum length be 3
ft. Let the circle on which O moves have a radius of 1.25 ft. Let the inclination angles θ
and φ of Figure P4.9.4 be:
π
θ = ( ) 3 cos π ( ) 6 t
and

φ = sin π
π ( ) 3 t
Find the velocity and acceleration of the rod center G and the rod extremity P for time t
equal to (a) 0, (b) 1, and (c) 2 sec, and express the results in terms of the unit vector sets
n , n , n and n , n , n , shown in Figure 4.9.4.
θ
x
z
z
y