Mechanical Vibration

Homework-2 MEE321 Summer 2018 Due: July 25th (Wednesday) in class

1) A unicycle has a suspension with spring constant k N/m, spring mass ms kg and damping ratio ξ. The tire has an original mass m1 kg and diameter e1 meter. An extra mass of debris m0 gram is stuck on the outermost part of the tire creating a mass unbalance. The weight of the person riding the unicycle is much greater than the weight of the unicycle. If the riding speed is speed v m/s, a) Draw a schematic of an equivalent system and find the induced amplitude of deflection of the tire (vertical direction) in the above scenario. You need not simplify the final expression but just be clear. [30 points] b) At what speed in m/s does the rider have to ride to hit the maximum possible deflection amplitude? And what is the value of that deflection? [10 points] [Hint: understand example 2.5.2 in the textbook] 2) An un-damped spring--mass system with spring constant 105 N/m and a mass of 4397.7 gram is harmonically excited by a force given by 𝐹 = 10 cos(𝜔𝑡) newton, where ω corresponds to a linear frequency of 24 rpm. For the initial values of 0.02 m displacement and 1 m/s velocity, plot the following using ‘subplot’ function in MATLAB

a) The full response of the system from 0 to 1 second. Show axes with units, labels, legend etc.

b) The particular response of the system from 0 to 1 second. Show axes with units, labels, legend etc.

Show your work and choice of equations etc. along with your MATLAB script and the plot in the homework. [20 points]