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Unformatted text preview: ME163 Mechanical Vibrations (Winter 2009) HW2 Due 1.22.09 in class25% if late within 24 hours50% if later than that 1. In order to experimentally determine the stiffness and damping coefficient of the system below, a bump test is performed. A bump test is a test which excites the dynamics in order to study its vibration. For this case the experimenter gave an initial condition in velocity as the ’bump’ and position and acceleration data was recorded of the movement. Considering that the mass is m = 20 [kg] address the questions below: (a) Construct a free body diagram and derive the equation of motion for the system. m ¨ x + c ˙ x + kx = 0 (b) Using the acceleration in plot 1, determine the natural frequency ω n . The initial condition for the simulation was { , 1 } and ω n = 2 . 0, ζ = 0 . 075, ω d = 1 . 994, c = 6, k = 80 (c) Calculate the effective stiffness k eff . k eff = 80 . (d) Using the position trace in plot 2 determine the damped natural frequency ω d . (e) Calculate the damping coefficient c . Consider plot 2 and measure two points of the wave at one period of distance. For example, let us take the first two peaks, and call them x 1 and x 2 . We can measure them and we see that x 1 = 0 . 45 m and x 2 = 0 . 28 m Using the logarithmic decrement method as in figure we have that the log decrement σ is σ = ln parenleftBig x 1 x 2 parenrightBig = ln( . 45 . 28 ) = 0 . 4745 , and from σ we can derive ξ as ξ = σ √ 4 π 2 + σ 2 = 0 . 0747 ≈ . 075 ....
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This note was uploaded on 03/23/2009 for the course ME 163 taught by Professor Mezic,i during the Winter '08 term at UCSB.
 Winter '08
 Mezic,I

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