EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 8220100254963
Author: Palm
Publisher: MCG
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Chapter 3, Problem 3.23P
For the geared system shown in Figure P3.23, assume that shaft inertias and the gear inertias
Figure P3.23
The speed ratios are
Derive the system model in terms of the speed
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find the laplace transform for the
flowing function
2(1-e)
Ans. F(s)=-
S
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k
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0 a
2a 3a 4a
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3
14) f(t)=1, 0
Find the solution of the following Differential Equations
Using Laplace Transforms
1) 4y+2y=0.
y(0)=2.
y'(0)=0.
2) y+w²y=0,
(0)=A,
y'(0)=B.
3) +2y-8y 0.
y(0)=1.
y'(0)-8.
4)-2-3y=0,
y(0)=1.
y'(0)=7.
5) y-ky'=0,
y(0)=2,
y'(0)=k.
6) y+ky'-2k²y=0,
y(0)=2,
y'(0) = 2k.
7) '+4y=0,
y(0)=2.8
8) y+y=17 sin(21),
y(0)=-1.
9) y-y-6y=0,
y(0)=6,
y'(0)=13.
10) y=0.
y(0)=4,
y' (0)=0.
11) -4y+4y-0,
y(0)=2.1.
y'(0)=3.9
12) y+2y'+2y=0,
y(0)=1,
y'(0)=-3.
13) +7y+12y=21e".
y(0)=3.5.
y'(0)=-10.
14) "+9y=10e".
y(0)=0,
y'(0)=0.
15) +3y+2.25y=91' +64.
y(0)=1.
y'(0) = 31.5
16)
-6y+5y-29 cos(2t).
y(0)=3.2,
y'(0)=6.2
17) y+2y+2y=0,
y(0)=0.
y'(0)=1.
18) y+2y+17y=0,
y(0)=0.
y'(0)=12.
19) y"-4y+5y=0,
y(0)=1,
y'(0)=2.
20) 9y-6y+y=0,
(0)-3,
y'(0)=1.
21) -2y+10y=0,
y(0)=3,
y'(0)=3.
22) 4y-4y+37y=0,
y(0)=3.
y'(0)=1.5
23) 4y-8y+5y=0,
y(0)=0,
y'(0)=1.
24)
++1.25y-0,
y(0)=1,
y'(0)=-0.5
25) y 2 cos(r).
y(0)=2.
y'(0) = 0.
26)
-4y+3y-0,
y(0)=3,
y(0) 7.
27) y+2y+y=e
y(0)=0.
y'(0)=0.
28) y+2y-3y=10sinh(27),
y(0)=0.
y'(0)=4.
29)…
Chapter 3 Solutions
EBK SYSTEM DYNAMICS
Ch. 3 - Prob. 3.1PCh. 3 - A baseball is thrown horizontally from the...Ch. 3 - For the mass shown in Figure 3.1.3b. m=10 kg, =25...Ch. 3 - A particle of mass m=19 kg slides down a...Ch. 3 - A particle of mass m slides down a frictionless...Ch. 3 - A radar tracks the flight of a projectile (see...Ch. 3 - Table 3.2.1 gives the inertia IO for a point mass...Ch. 3 - A motor supplies a moment M to the pulley of...Ch. 3 - Figure P3.9 shows an inverted pendulum. Obtain the...Ch. 3 - The two masses shown in Figure P3.10 are released...
Ch. 3 - The motor in Figure P3.11 lifts the mass mL by...Ch. 3 - Instead of using the system shown in Figure 3.2.6a...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Derive the expression for the equivalent inertia...Ch. 3 - Prob. 3.18PCh. 3 - The geared system shown in Figure P3.19 represents...Ch. 3 - Prob. 3.20PCh. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - For the geared system shown in Figure P3.23,...Ch. 3 - For the geared system discussed in Problem 3.23,...Ch. 3 - The geared system shown in Figure P3.25 is similar...Ch. 3 - Consider the rack-and-pinion gear shown in Figure...Ch. 3 - The lead screw (also called a power screw or a...Ch. 3 - Prob. 3.29PCh. 3 - Derive the equation of motion of the block of mass...Ch. 3 - Assume the cylinder in Figure P3.31 rolls without...Ch. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - A slender rod 1.4 m long and of mass 20 kg is...Ch. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - The pendulum shown in Figure P3.38 consists of a...Ch. 3 - Prob. 3.39PCh. 3 - A single link of a robot arm is shown in Figure...Ch. 3 - 3.41 It is required to determine the maximum...Ch. 3 - Figure P3.42 illustrates a pendulum with a base...Ch. 3 - Figure P3.43 illustrates a pendulum with a base...Ch. 3 - 3.44 The overhead trolley shown in Figure P3.44 is...Ch. 3 - Prob. 3.45PCh. 3 - The “sky crane” shown on the text cover was a...
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