Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 18.4, Problem 1PP
Determine the kinetic energy of the 100-kg object.
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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)…
Auto Controls
A union feedback control system has the following open loop transfer function
where k>0 is a variable proportional gain
i. for K = 1 , derive the exact magnitude and phase expressions of G(jw).
ii) for K = 1 , identify the gaincross-over frequency (Wgc) [where IG(jo))| 1] and phase cross-overfrequency [where <G(jw) = - 180]. You can use MATLAB command "margin" to obtain there quantities.
iii) Calculate gain margin (in dB) and phase margin (in degrees) ·State whether the closed-loop is stable for K = 1 and briefly justify your answer based on the margin . (Gain marginPhase margin)
iv. what happens to the gain margin and Phase margin when you increase the value of K?you
You can use for loop in MATLAB to check that.Helpful matlab commands : if, bode, margin, rlocus
NO COPIED SOLUTIONS
Chapter 18 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 18.4 - Determine the kinetic energy of the 100-kg object.Ch. 18.4 - The 80-kg wheel has a radius of gyration about its...Ch. 18.4 - The uniform 50-lb slender rod is subjected to a...Ch. 18.4 - The uniform 50-kg slender rod is at rest m the...Ch. 18.4 - The 50-kg wheel is subjected to a force of 50 N....Ch. 18.4 - If the uniform 30-kg slender rod starts from rest...Ch. 18.4 - The 20-kg wheel has a radius of gyration about its...Ch. 18.4 - At a given instant the body of mass m has an...Ch. 18.4 - The wheel is made from a 5-kg thin ring and two...Ch. 18.4 - The wheel is made from a 5-kg thin ring and two...
Ch. 18.4 - A force of P = 60 N is applied to the cable, which...Ch. 18.4 - A force of P = 20 N is applied to the cable, which...Ch. 18.4 - A force of P = 20 N is applied to the cable, which...Ch. 18.4 - The double pulley consists of two parts that are...Ch. 18.4 - The double pulley cons1sts of two parts that are...Ch. 18.4 - Prob. 9PCh. 18.4 - The spool has a mass of 40 kg and a radius of...Ch. 18.4 - Prob. 11PCh. 18.4 - Determine the velocity of the 50-kg cylinder after...Ch. 18.4 - The 10-kg uniform slender rod is suspended at rest...Ch. 18.4 - Prob. 14PCh. 18.4 - The pendulum consists of a 10-kg uniform disk and...Ch. 18.4 - A motor supplies a constant torque M = 6 kNm to...Ch. 18.4 - The center O of the thin ring of mass m is given...Ch. 18.4 - Prob. 18PCh. 18.4 - Prob. 19PCh. 18.4 - If P = 200 N and the 15-kg uniform slender rod...Ch. 18.4 - A yo-yo has a weight of 0.3 lb and a radius of...Ch. 18.4 - Prob. 22PCh. 18.4 - Prob. 23PCh. 18.4 - Prob. 24PCh. 18.4 - The 30-kg disk is originally at rest, and the...Ch. 18.4 - Two wheels of negligible weight are mounted at...Ch. 18.4 - Prob. 27PCh. 18.4 - The 10-kg rod AB is pin connected at A and...Ch. 18.4 - The 10-lb sphere starts from rest at = 0 and...Ch. 18.4 - Motor M exerts a constant force of P = 750 Non the...Ch. 18.4 - Prob. 31PCh. 18.4 - The linkage consists of two 6-kg rods AB and CD...Ch. 18.4 - The two 2-kg gears A and B are attached to the...Ch. 18.4 - The linkage consists of two 8-lb rods AB and CD...Ch. 18.4 - The linkage consists of two 8-lb rods AB and CD...Ch. 18.5 - F187. If the 30-kg disk is released from rest when...Ch. 18.5 - The 50-kg reel has a radius of gyration about its...Ch. 18.5 - The 60-kg rod OA is released from rest when = 0....Ch. 18.5 - Prob. 10FPCh. 18.5 - The 30-kg rod is released from rest when = 45....Ch. 18.5 - Prob. 12FPCh. 18.5 - Prob. 36PCh. 18.5 - Prob. 37PCh. 18.5 - An automobile tire has a mass of 7 kg and radius...Ch. 18.5 - The spool has a mass of 20 kg and a radius of...Ch. 18.5 - The spool has o mass of 20 kg and a radius of...Ch. 18.5 - A uniform ladder having a weight of 30 lb is...Ch. 18.5 - Prob. 44PCh. 18.5 - The 12-kg slender rod is attached to a spring,...Ch. 18.5 - Prob. 46PCh. 18.5 - The 40-kg wheel has a radius of gyration about its...Ch. 18.5 - The assembly consists of two 10-kg bars which are...Ch. 18.5 - The assembly consists of two 10-kg bars which are...Ch. 18.5 - The compound disk pulley consists of a hub and...Ch. 18.5 - Prob. 51PCh. 18.5 - Prob. 52PCh. 18.5 - The two 12-kg slender rods are pin connected and...Ch. 18.5 - If the 250-lb block is released from rest when the...Ch. 18.5 - The slender 15-kg bar is initially at rest and...Ch. 18.5 - If the chain is released from rest from the...Ch. 18.5 - Prob. 57PCh. 18.5 - Prob. 58PCh. 18.5 - The slender 6-kg bar AB is horizontal and at rest...Ch. 18.5 - Prob. 60PCh. 18.5 - Prob. 61PCh. 18.5 - The 50-lb wheel has a radius of gyration about its...Ch. 18.5 - The system consists of 60-lb and 20-lb blocks A...Ch. 18.5 - The door is made from one piece, whose ends move...Ch. 18.5 - Prob. 65PCh. 18.5 - Prob. 66PCh. 18.5 - Prob. 67PCh. 18.5 - The system consists of a 30-kg disk A, 12-kg...Ch. 18.5 - The pendulum of the Charpy impact machine has a...Ch. 18.5 - Prob. 2RPCh. 18.5 - The drum has a mass of 50 kg and a radius of...Ch. 18.5 - The spool has a mass of 60 Kg and a radius of...Ch. 18.5 - Prob. 5RPCh. 18.5 - At the Instant shown, the 50-lb bar rotates...Ch. 18.5 - Prob. 7RPCh. 18.5 - Prob. 8RP
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- The 120 kg wheel has a radius of gyration of 0.7 m. A force P with a magnitude of 50 N is applied at the edge of the wheel as seen in the diagram. The coefficient of static friction is 0.3, and the coefficient of kinetic friction is 0.25. Find the acceleration and angular acceleration of the wheel.arrow_forwardAuto Controls Using MATLAB , find the magnitude and phase plot of the compensators NO COPIED SOLUTIONSarrow_forward4-81 The corner shown in Figure P4-81 is initially uniform at 300°C and then suddenly exposed to a convection environment at 50°C with h 60 W/m². °C. Assume the = 2 solid has the properties of fireclay brick. Examine nodes 1, 2, 3, 4, and 5 and deter- mine the maximum time increment which may be used for a transient numerical calculation. Figure P4-81 1 2 3 4 1 cm 5 6 1 cm 2 cm h, T + 2 cmarrow_forward
- Auto Controls A union feedback control system has the following open loop transfer function where k>0 is a variable proportional gain i. for K = 1 , derive the exact magnitude and phase expressions of G(jw). ii) for K = 1 , identify the gaincross-over frequency (Wgc) [where IG(jo))| 1] and phase cross-overfrequency [where <G(jw) = - 180]. You can use MATLAB command "margin" to obtain there quantities. iii) Calculate gain margin (in dB) and phase margin (in degrees) ·State whether the closed-loop is stable for K = 1 and briefly justify your answer based on the margin . (Gain marginPhase margin) iv. what happens to the gain margin and Phase margin when you increase the value of K?you You can use for loop in MATLAB to check that.Helpful matlab commands : if, bode, margin, rlocus NO COPIED SOLUTIONSarrow_forwardAuto Controls Hand sketch the root Focus of the following transfer function How many asymptotes are there ?what are the angles of the asymptotes?Does the system remain stable for all values of K NO COPIED SOLUTIONSarrow_forward-400" 150" in Datum 80" 90" -280"arrow_forward
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