me445_hw1 - illustrated below The purpose of the spring is...

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ME 445 Mechanical Vibrations // Fall 2009 Homework #1 1. Solve mx" + kx = 0 for k = 4 N/m, m = 1 kg, x 0 = 1 mm, and v 0 = 0. Plot the solution. 2. 3. An automobile is modeled as a 1000-kg mass supported by a spring of stiffness k = 400,000 N/m. When it oscillates it does so with a maximum deflection of 10 cm. When loaded with passengers, the mass increases to as much as 1300 kg. Calculate the change in frequency, velocity amplitude, and acceleration amplitude if the maximum deflection remains 10 cm. 4. A foot pedal mechanism for a machine is crudely modeled as a pendulum connected to a spring as
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Unformatted text preview: illustrated below. The purpose of the spring is to keep the pedal roughly vertical. Compute the spring stiffness needed to keep the pendulum at 1° from the horizontal and then compute the corresponding natural frequency. Assume that the angular deflections are small, such that the spring deflection can be approximated by the arc length, that the pedal may be treated as a point mass and that pendulum rod has negligible mass. The values in the figure are m =0.5 kg, g =9.8 m/s 2 , l 1 = 0.2 m and l 2 = 0.3 m. 5....
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