Homework 5

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School

Lone Star College, CyFair *

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Course

365

Subject

Mechanical Engineering

Date

Oct 30, 2023

Type

pdf

Pages

2

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ASE 365: Problem Set 5 Due date: 13 October 2023 1. The control tab is being forced by a harmonic displacement y(t) . If resonance occurs at a frequency w = w r , find the torsional stiffness k T at the hinge O in terms of the parameters given. 2. Consider the car from Prob. 5, Homework 4 (mass = 1000kg, suspension stiffness = 400 kN/m and damping = 20kN.s/m), traveling over a bumpy road as shown below. The bumps can be approximated by a half-cycle of a sine wave (the negative half-cycles are zero). Determine the amplitude of vibration of the car if it is traveling at a velocity of 20 km/hr. How is this response different from that of Prob. 5, Homework 4? 3. Consider the square wave forcing shown below. Plot the forcing including (a) only first three harmonics (b) first five harmonics (c) first 10 harmonics. What do you conclude from this?
4. Let the forcing in Problem 3 be applied to a mass-spring-damper system with z =0.2 and natural frequency = p /T . Derive the response of the system and plot it for (a) first three harmonics (b) first five harmonics (c) first ten harmonics.
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