Chapter 4 Single Degree-of-Freedom Vibration: General Loading and Advanced Topics
Problems for Section 4.1 Arbitrary Loading: Laplace Transform 1. Solve the following equations of motion using the Laplace transform approach: (a) y + 2y + 3y = 5 cos 3t; y
Chapter 2 Single Degree-of-Freedom Vibration: Discrete Models
Problems for Section 2.2 Math Modeling: Deterministic 1. The beam in Figure 2.26 vibrates as a result of loading not shown. State the necessary assumptions to reduce this problem to a one degre
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CHAPTER 2 SDOF VIBRATION: AN INTRODUCTION
By the energy method, we substitute the kinetic and potential energies into the principle of the conservation of energy. 1 _2 I ; V = mgl cos 2 12 T +V = I_ mgl cos = const: 2 T= Dierentiating the total energy
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2. Derive Equation 3.3: x(t) = Ce
!n t
cos(! d t
): < 1 (since this
Solution: This equation is derived by rewriting the general solution for the case is an oscillatory solution). We write Equation 3.2 as p2 p2 x (t) = e !n t A1 ei 1 !n t + A2 e i 1 !n t
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CHAPTER 3 SDOF VIBRATION: WITH DAMPING
4. For a mass-spring-damper system in free vibration: (a) Derive the equation of motion and solve for the transient response x(t) that is driven by the initial conditions x(0) = x0 and x(0) = v0 . (b) Assume parame
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8. Estimate the number of cycles n required for a structural oscillation amplitude to decay to x% of its maximum. (a) What is the expression for the logarithmic decrement in terms of n and x? (b) Solve for n in terms of and x. (c) Plot n as a function
Chapter 8 Multi Degree-of-Freedom Vibration: Introductory Topics
Problems for Section 8.2 The Concepts of Stiness and Flexibility
1. The two degree-of-freedom system in Figure 8.38 undergoes translational motion. (a) Derive the exibility in uence coe cien