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11 Pages

### SolSec 2.4

Course: MECHANICAL MAE351, Spring 2009
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Word Count: 1492

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27 2- Problems and Solutions Section 2.4 (2.37 through 2.50) 2.37 A machine weighing 2000 N rests on a support as illustrated in Figure P2.37. The support deflects about 5 cm as a result of the weight of the machine. The floor under the support is somewhat flexible and moves, because of the motion of a nearby machine, harmonically near resonance (r =1) with an amplitude of 0.2 cm. Model the floor as base motion,...

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Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
2- 39 Problems and Solutions Section 2.5 (2.51 through 2.58) 2.51 A lathe can be modeled as an electric motor mounted on a steel table. The table plus the motor have a mass of 50 kg. The rotating parts of the lathe have a mass of 5 kg at a distance 0
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
2-42 Problems and Solutions Section 2.6 (2.59 through 2.62) 2.59 Calculate damping and stiffness coefficients for the accelerometer of Figure 2.23 with moving mass of 0.04 kg such that the accelerometer is able to measure vibration between 2 0 and 50
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
2-44 Problems and Solutions Section 2.7 (2.63 through 2.79) 2.63 Consider a spring-mass sliding along a surface providing Coulomb friction, with stiffness 1.2 10 4 N/m and mass 10 kg, driven harmonically by a force of 50 N at 10 Hz. Calculate the ap
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
2- 60Problems and Solutions Section 2.8 (2.80 through 2.86) 2.80*. Numerically integrate and plot the response of an underdamped system determined by m = 100 kg, k = 20,000 N/m, and c = 200 kg/s, subject to the initial conditions of x0 = 0.01 m and
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
2- 69Problems and Solutions Section 2.9 (2.87 through 2.93) 2.87*. Compute the response of the system in Figure 2.34 for the case that the damping is linear viscous and the spring is a nonlinear soft spring of the form k(x) = kx ! k1 x 3 and the sy
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions Section 1.1 (1.1 through 1.19) 1.1 The spring of Figure 1.2 is successively loaded with mass and the corresponding (static) displacement is recorded below. Plot the data and calculate the spring's stiffness. Note that the data
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions for Section 1.2 and Section 1.3 (1.20 to 1.51) Problems and Solutions Section 1.2 (Numbers 1.20 through 1.30) 1.20* Plot the solution of a linear, spring and mass system with frequency n =2 rad/s, x0 = 1 mm and v0 = 2.34 mm/s,
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions Section 1.4 (problems 1.52 through 1.65) 1.52 Calculate the frequency of the compound pendulum of Figure 1.20(b) if a mass mT is added to the tip, by using the energy method. Solution Using the notation and coordinates of Figur
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions Section 1.5 (1.66 through 1.74) 1.66 A helicopter landing gear consists of a metal framework rather than the coil spring based suspension system used in a fixed-wing aircraft. The vibration of the frame in the vertical directio
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions Section 1.6 (1.75 through 1.81) 1.75 Show that the logarithmic decrement is equal to!=1 x0 ln n xnwhere xn is the amplitude of vibration after n cycles have elapsed. Solution:'() t ! ! xt \$ Ae n sin ) d t + * # ln # &amp; =
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions Section 1.7 (1.82 through 1.89) 1.82 Choose a dashpot's viscous damping value such that when placed in parallel with the spring of Example 1.7.2 reduces the frequency of oscillation to 9 rad/s. Solution: The frequency of oscill
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions Section 1.8 (1.90 through 1.93) 1.90 Consider the system of Figure 1.90 and (a) write the equations of motion in terms of the angle, , the bar makes with the vertical. Assume linear deflections of the springs and linearize the
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions Section 1.9 (1.94 through 1.101) 1.94* Reproduce Figure 1.38 for the various time steps indicated. Solution: The code is given here in Mathcad, which can be run repeatedly with different t to see the importance of step size. Ma
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions Section 1.10 (1.102 through 1.114) 1.102 A 2-kg mass connected to a spring of stiffness 103 N/m has a dry sliding friction force (Fc) of 3 N. As the mass oscillates, its amplitude decreases 20 cm. How long does this take? Solut
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions for Section 4.1 (4.1 through 4.16) 4.1 Consider the system of Figure P4.1. For c1 = c2 = c3 = 0, derive the equation of motion and calculate the mass and stiffness matrices. Note that setting k3 = 0 in your solution should resu
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions for Section 4.2 (4.19 through 4.33) 4.19 Calculate the square root of the matrix&quot; 13 !10 % M=\$ ' # !10 8 &amp;&quot; &quot; a !b % 1/ 2 1/ 2 \$ Hint: Let M = \$ ' ; calculate M !b c &amp; # #()2% and compare to M.' &amp;Solution: Given:&quot;
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions for Section 4.3 (4.34 through 4.43) 4.34 Solve Problem 4.11 by modal analysis for the case where the rods have equal stiffness! (i.e., k1 = k2 ), J1 = 3J 2 , and the initial conditions are x(0) = !0 1# and x 0 = 0. &quot; \$T()
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions for Section 4.4 (4.44 through 4.55) 4.44 A vibration model of the drive train of a vehicle is illustrated as the three-degreeof-freedom system of Figure P4.44. Calculate the undamped free response [i.e. ! M(t) = F(t) = 0, c1 =
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions for Section 4.5 (4.56 through 4.66) 4.56 Consider the example of the automobile drive train system discussed in Problem 4.44. Add 10% modal damping to each coordinate, calculate and plot the system response. Solution: Let k1 =
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions for Section 4.6 (4.67 through 4.76) 4.67 Calculate the response of the system of Figure 4.16 discussed in Example 4.6.1 if F1(t) = (t) and the initial conditions are set to zero. This might correspond to a two-degree-of-freedom
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions for Section 4.7 (4.76 through 4.79) 4.76 Use Lagrange's equation to derive the equations of motion of the lathe of Fig. 4.21 for the undamped case. Solution: Let the generalized coordinates be !1 ,! 2 and ! 3 . The kinetic ener
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions for Section 4.9 (4.80 through 4.90) 4.80 Consider the mass matrix &quot;10 !1% M=\$ ' # !1 1 &amp; and calculate M-1, M-1/2, and the Cholesky factor of M. Show that LLT = MM !1/ 2 M !1/ 2 = I M 1/ 2 M 1/ 2 = MSolution: Given&quot;10 !1% M
Korea Advanced Institute of Science and Technology - MECHANICAL - MAE351
Problems and Solutions Section 4.10 (4.91 through 4.98) 4.91* Solve the system of Example 1.7.3 for the vertical suspension system of a car with m = 1361 kg, k = 2.668 x 105 N/m, and c = 3.81 x 104 kg/s subject to the initial conditions of x(0) = 0 a
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1ACCT 2301 Spring Semester 2009 February 9, 2009Practice Problems Process Costing 1. Amarillo Company uses the weighted-average method in its process costing system. A total of 254,000 units were transferred in to the Assembly Department from th
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1ACCT 2301 Spring Semester 2009 February 24, 2009Practice Problems Activity-Based Costing 1. If substantial batch-level or product-level costs exist, then overhead allocation based solely on a measure of volume such as direct labor-hours: A. B.
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ACCT2301 Spring Semester 2009 First Interim Exam January 29, 2009 FORMAName Student 10 ~'*&lt;I,.) -tl~-C \)PART 1- Multiple Choice (28 questions at 3 points each). Select the BEST answerfor each question and indicate your selecti
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