System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 7, Problem 7.25P
Design a piston-type damper using an oil with a viscosity at 20°C of // 0.9 kg/(m • s). The desired damping coefficient is 2000 N • s/m. See Figure 7.4.4.
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A linear harmonic oscillator having a mass of 3.0kg is set into motion with viscous damping. if the frequency is 12HZ and if two successive
amplitudes a full cycle apart are measured to be 4.65mm and 4.30mm, compute the viscous damping coefficient.
Note: Give your answer to 3 decimal places
x (t)
Other Parameters:
Logarithmic Decrement (6):
Answer:
x2
X,
-In1
X2
21 C
8 = In
=5wn Td = 5wn
%3D
Xn+1
a2m
Damping Ratio (5): 5 =
%3D
t [s]
2vkm
Cc
2man
Frequency of damped vibration (wa): wa =
Undamped Forced Vibration:
Fo/k
Frequency Ratio (r): r -
p-xsin wt
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A linear harmonic oscillator having a mass of 5.4kg is set into motion with viscous damping. if the frequency is 7Hz and if two successive
amplitudes a full cycle apart are measured to be 4.65mm and 4.30mm, compute the viscous damping coefficient.
Note: Give your answer to 3 decimal places
Other Parameters:
x (t)
Logarithmic Decrement (6):
Answer:
x2
2nC
2n C
2T
8 = In1 = In1 = 5 wnTd = 5 wn
%3D
X3
X2
Xn+1
uz Pm
Damping Ratio (5): 5 =
%3D
t [s]
(2T)2+8
Cc
2vkm
2mwn
Wn
Frequency of damped vibration (wa): wa =
Undamped Forced Vibration:
Fo/k
x sin ot
Frequency Ratio (r): r =
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E//learnonline.gmit.ie/mod/quiz/attempt.php?attempt3D167036&cmid%3D155306&page%3D2...
P Type here to search
3| 5
Q.5 A seismometer has a natural frequency of 8 Hz and a damping ratio of 0.2. What is
the percentage error in measuring the amplitude at frequency f= 160 Hz?
Chapter 7 Solutions
System Dynamics
Ch. 7 - Prob. 7.1PCh. 7 - Refer to the water storage and supply system shown...Ch. 7 - Prob. 7.3PCh. 7 - In Figure P7.4 the piston of area A is connected...Ch. 7 - Refer to Figure 7.1.4a. and suppose that p\ — p2=...Ch. 7 - Pure water flows into a mixing tank of volume V =...Ch. 7 - Consider the mixing tank treated in Problem 7.6....Ch. 7 - Derive the expression for the fluid capacitance of...Ch. 7 - Prob. 7.9PCh. 7 - Prob. 7.10P
Ch. 7 - 7.11 Derive the expression for the capacitance of...Ch. 7 - Air flows in a certain cylindrical pipe 1 m long...Ch. 7 - Derive the expression for the linearized...Ch. 7 - Consider the cylindrical container treated in...Ch. 7 - A certain tank has a bottom area A = 20 m2. The...Ch. 7 - A certain tank has a circular bottom area A = 20...Ch. 7 - The water inflow rate to a certain tank was kept...Ch. 7 - Prob. 7.18PCh. 7 - Prob. 7.19PCh. 7 - In the liquid level system shown in Figure P7.20,...Ch. 7 - The water height in a certain tank was measured at...Ch. 7 - Derive the model for the system shown in Figure...Ch. 7 - (a) Develop a model of the two liquid heights in...Ch. 7 - Prob. 7.24PCh. 7 - Design a piston-type damper using an oil with a...Ch. 7 - Prob. 7.26PCh. 7 - 7.27 An electric motor is sometimes used to move...Ch. 7 - Prob. 7.28PCh. 7 - Prob. 7.29PCh. 7 - Figure P7.3O shows an example of a hydraulic...Ch. 7 - Prob. 7.31PCh. 7 - Prob. 7.32PCh. 7 - Prob. 7.33PCh. 7 - Prob. 7.34PCh. 7 - Prob. 7.35PCh. 7 - Prob. 7.36PCh. 7 - Prob. 7.37PCh. 7 - (a) Determine the capacitance of a spherical tank...Ch. 7 - Obtain the dynamic model of the liquid height It...Ch. 7 - Prob. 7.40PCh. 7 - Prob. 7.41PCh. 7 - Prob. 7.42PCh. 7 - Prob. 7.43PCh. 7 - Prob. 7.44PCh. 7 - Prob. 7.45PCh. 7 - The copper shaft shown in Figure P7.46 consists of...Ch. 7 - A certain radiator wall is made of copper with a...Ch. 7 - A particular house wall consists of three layers...Ch. 7 - A certain wall section is composed of a 12 in. by...Ch. 7 - Prob. 7.50PCh. 7 - Prob. 7.51PCh. 7 - A steel tank filled with water has a volume of...Ch. 7 - Prob. 7.53PCh. 7 - Prob. 7.54PCh. 7 - Prob. 7.55P
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Determine č, wa and free Vibration response of viscously damped system for initial conditions xo= 0.1 m and x o = 10 m/s with m=10 Kg, c= 250 N-s/m & k=1000 N/m. Solution#4 (to be typed here by the student)arrow_forwardFor a spring mass damper system, m = 50 kg, k = 5000 N/m and C = 2Cc. Find the following: (a) Critical damping coefficient (b) Damped natural frequency (c) Logarithmic decrementarrow_forwardA vertical spring-mass system is submerged in oil. The spring has a stiffness coefficient of 3 N/m, and the mass is 1 kg. If the dampened angular frequency omega_d of oscillation is 0.866 Hz, find the damping coefficient b for the oil and how long it takes the spring to reach 50 percent of its original amplitude.arrow_forward
- Please full solution with the drawing. Big and clear handwritingarrow_forwardDetermine the value of the viscous damping coefficient c for which the system shown is critically damped. Use k = 35 kN/m, m = 100 kg. k m Insert your answer for c in N. s/m correct up to at least a third decimal place.arrow_forwardAnswer completely.arrow_forward
- A single degree of freedom mass-spring-damper system is subject to vibration under the influence of a harmonic force. On my site, it is given as m=2 kg, k=800 N/m, c=64 Ns/m. The amplitude of the harmonic force is F0=256 N and its frequency is w= 20 rad/s. Answer the questions in options a, b, and c according to the given information. 1) Calculate the damping ratio of the system (ξ) a.1 b.0.7 c.0.9 d.0.8 2)Calculate the magnification factor (M) of the system. a.0.86 b.1.25 c.0.312 D.0.625 3-) Calculate the maximum vibration amplitude (X) (meters). a.0.2 b.0.1 c.0.4 D.0.3arrow_forward3arrow_forwardFor the system: x:(t) f(t) M1 surface friction - f, = 6.0 Nm/s Find an equation that relates settling time of the velocity of the mass to M. b. Find an equation that relates rise time of the velocity of the mass to M.arrow_forward
- 3. Determine the viscosity of the fluid that one needs to use to realize a parallel-plate damper when the top plate has an area of 0.02 m², the gap between the parallel plates h = 0.2 mm, and the required damping coefficient is 20 N s/m.arrow_forwardpart 3 4 and 5 please of this questionarrow_forwardProblem 3: Leaking Tank Your engineering firm has been asked to determine whether the secondary clarifier (labeled "SECONDARY") downstream from the aeration basin (labeled "AERATION") is leaking at your local wastewater treatment plant. You conduct measurements over 45 minutes. During this time, you determine the average inflow rate Qin = 4.5 m³/min, the average outflow rate Qout = 4.0 m³/min, and the change in volume in the secondary clarifier is AV = 2.2 m³. You also determine that the fluid removed from the aeration basin is 90% water and 10% air by volume, since the fluid contains air bubbles. These bubbles rapidly dissipate in the secondary clarifier. PRETREATMENT OVERFLOW SECONDARY SLUDGE DIGESTION TRASH DRYER AERATION AIR PRIMARY DRY SLUDGE FINISHING ALICANTOY Is the secondary clarifier leaking, and if so, at what rate? [kg/min] SCUM METHANEarrow_forward
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