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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An application demands that sinusoidal pressure variation
of 250 Hz be measured with no more than 2% dynamic
error. In selecting a suitable pressure transducer from
vendor catalog, you note that a desirable line of
transducer has a fixed natural frequency of 500 Hz but
that you have a choice of transducer damping ratio of
between 0.5 and 1.5 in increments of 0.05. select a
suitable transducer.
The value of damping that can be chosen from the
catalog
Select one:
a. 0.65
b. 0.35
O c. 0.55
d. 0.75
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 =
Next page
jous page
E//learnonline.gmit.ie/mod/quiz/attempt.php?attempt3D167036&cmid%3D155306&page%3D2...
P Type here to search
3| 5
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
- 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?arrow_forwardDetermine 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_forwardAn application demands that sinusoidal pressure variation of 250 Hz be measured with no more than 2% dynamic error. In selecting a suitable pressure transducer from vendor catalog, you note that a desirable line of transducer has a fixed natural frequency of 500 Hz but that you have a choice of transducer damping ratio of between 0.5 and 1.5 in increments of 0.05. select a suitable transducer. The value of damping ratio is between the following values Select one: a. 0.707 and 0.807 b. 0.5215 and 0.5625 c. 0.631 and 0.692 d. 0.2356 and 0.5625arrow_forward
- Q2. For a base motion system described by with mä +ci + kx = cYw,cosw, t + kYsin wht m = 100 kg, c = 50 kg/s, k = 1000 N/m, Y = 0.03 m and w, = 3 rad/s. calculate the %3D magnitude of the particular solution and compute the transmissibility ratio.arrow_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_forward2.10 Derive the equation for the displacement response of a viscously damped SDF system due to ini- tial velocity u(0) for three cases: (a) underdamped systems; (b) critically damped systems; and (c) overdamped systems. Plot u(t) : u(0)/w, against t/T, for 5 =0.1, 1, and 2.arrow_forward
- For 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_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_forwardProblem 7: A small ball bearing is released from rest in a tank of oil at t = 0. The downward acceleration of the ball bearing is g - kv, where g is the constant acceleration due to gravity, k is a constant that depends on the viscosity of the oil, and is the downward velocity of the object. Derive expressions for the velocity and the displacement y as function of the time t after the ball bearing's release. Ans (partial): v = g(1 - e-kt)/karrow_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_forwardDetermine the value of the viscous damping coefficient c for which the system shown is critically damped. Use k = 45 kN/m, m = 80 kg. k т Insert your answer for c in N. s/m correct up to at least a third decimal place.arrow_forwardConsider the system presented in the following figure K, = 500N / m K, = 2000N / m M = 1Kg %3D X, = 20mm %3D Vo = Omm/s %3D The stiffness of the equivalent spring (in N/m) is equal to Choose... The natural frequency in rad/s is equal to The amplitude of vibration (in m) is Choose... Choose... The phase shift of the vibration is Choose...arrow_forward
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