# a4 - proximated by a cosine function with 20m separating...

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Phys 263/Amath 261 Assignment 4 Due: Wednesday, June 11, 2008 (in class) 1. A van of mass 10 3 kg, when stationary on level ground, compresses its suspension springs by 10cm. Neglect the mass of the wheels, and anything else that is not supported by the suspension. (a) Calculate the eﬀective spring constant k , i.e. that resulting from considering the mass of the truck compressing a single spring by 10cm. (b) Calculate the undamped oscillation period. (c) Shock absorbers (dampers) are ﬁtted to provide critical damping. Calculate the damping constant b . (d) The van is now loaded with an additional 3 × 10 3 kg. Calculate the new values, ω 0 0 and γ 0 , of the free oscillation angular frequency and damping parameter. Is the new system under, over, or critical damped? (e) Calculate the oscillation period of the loaded van. (f) The loaded van drives at a constant speed along a road with a series of speed bumps (which provide a vertical periodic force). Assume that these can be ap-
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Unformatted text preview: proximated by a cosine function with 20m separating the peaks. With what speed is the van travelling when resonance occurs between the bumps and the suspension? 2. A block of mass 2 kg is attached to a spring of strength 2000 N m-1 . The block is subject to a driving force 36 cos( t ) N. Given that the spring will break if it is extended more than 3 cm past its equilibrium position, nd the range of frequencies that can safely be applied. 3. For the two-dimensional simple harmonic oscillator with equations of motion x ( t ) = cos( x t- ) y ( t ) = cos( y t- ) Plot Lissajous curves (the paths of motion in x-y space) for the following cases: (a) x = 1, y = 2, and = / 5 and = 0. (b) x = 5, y = 4, and = and = / 2. (c) x = 10, y = 11, and = / 2 and = . (d) x = , y = 1, and = 0 and = 0. What is dierent about this case? 1...
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## This note was uploaded on 09/20/2010 for the course AMATH 261 taught by Professor Rogermelko during the Spring '10 term at Waterloo.

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