Theory of Vibration An Introduction 3rd. Edition by Ahmed A. Shabana | 9783319942704 | 3319942700 | Holooly

Mechanical Engineering

Theory of Vibration An Introduction

59 SOLVED PROBLEMS

Question: 5.4

Determine the steady state response of the single degree of freedom system shown in Fig. 5.7, due to the periodic forcing function F(t) given in Example 5.2. Neglect the gravity effect. ...

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The equation of motion of this system is given by ...

Question: 5.8

Use the method of the numerical evaluation of the Duhamel integral discussed in this section to obtain the dynamic response of the single degree of freedom system of Example 5.6. Assume thatm = 1 kg, k = 2500 N/m, c = 10N·s/m, F_{0} = 10 N. ...

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The natural frequency of the system ω ω =

\...

Question: 3.4

Figure 3.11(a) shows a pendulum which is supported by two springs which have stiffness coefficients k1 and k2. The two springs are connected to the pendulum rod at points which are at distances a and b from the pin joint, as shown in the figure. If the two springs shown in Fig. 3.11(a) are to be ...

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As shown in Fig. 3.11(c), the force produced by th...

Question: 3.12

The following data are given for a damped single degree of freedom mass– spring system, mass m = 5 kg, damping coefficient c = 20 N · s/m, and stiffness coefficient k = 5 × 10³ N/m. The mass is subjected to a force which depends on the velocity and can be written as F = bx , where b is a constant. ...

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The equation of motion of the system is

m\d...

Question: 3.13

Figure 3.21 shows two masses m1 and m2 where m1 = 5 kg and m2 = 1 kg. The mass m1 which is initially at rest is supported by a spring and a damper. The stiffness coefficient of the spring k is assumed to be 1000 N/m, and the damping coefficient c is assumed to be 10 N · s/m. ...

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The conservation of momentum and the restitution c...

Question: 1.3

Figure 1.14 depicts a rigid rod of length l, mass m, and mass moment of inertia about its mass center, Ic. One end of the rod is connected to the ground by a pin joint, and the other end is connected to the ground by spring and damper. The spring stiffness is k and the viscous damping coefficient is c. If T is an ...

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For a given angular orientation θ, the free body d...

Question: 6.10

Determine the steady state response of the two degree of freedom system shown in Fig. 6.11, assuming small oscillations. ...

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Assuming

θ_{2} > θ_{1}

and [late...

Question: 5.7

Find the forced response of the undamped single degree of freedom system to the forcing function shown in Fig. 5.13. ...

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The forced response of the undamped single degree ...

Question: 4.6

The damped single degree of freedom mass–spring system shown in Fig. 4.15 has a mass m = 25 kg, and a spring stiffness coefficient k = 2500 N/m. Determine the damping coefficient of the system knowing that the mass exhibits an amplitude of 0.01m when the support oscillates at the natural ...

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From Eq. 4.98, the amplitude of the oscillation of...

Question: 5.5

Find the response of the single degree of freedom system shown in Fig. 5.9 to the rectangular impulsive force shown in Fig. 5.8, where m = 10 kg, k = 9,000 N/m, c = 18N · s/m, and F0 = 10,000 N. The force is assumed to act at time t = 0 and the impact interval is assumed to be 0.005 s. ...

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The linear impulse I is given by I =

\int_ ...

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