chap_VI_hwk_fall_2010

chap_VI_hwk_fall_2010 - Vibrations Homework Problems ME 274...

This preview shows pages 1–4. Sign up to view the full content.

Vibrations Homework Problems ME 274 Problem VI-1 A homogeneous drum (of mass m and outer radius R) rolls without slipping on a rough horizontal surface. A spring of stiffness k is attached between the center O of the drum and ground such that the spring remains horizontal at all time. Block A (of mass m) is connected to O through an inextensible cable as shown in the figure. Let x represent the motion of O (measured positively to the right) with the spring being unstretched when x = 0. Assume that the cable does not go slack at any time. a) Draw individual free body diagrams of the disk and of block A. b) Derive the single differential equation of motion (EOM) for the system in terms of the coordinate x, its time derivatives and, at most, the following parameters: g , m and k . k g x + R A m m no slip O

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Vibrations Homework Problems ME 274 Problem VI-2 A homogeneous disk having a mass of m and outer radius R is supported by a cable. This cable is attached to ground at end B and attached to a spring at end E. This spring has a stiffness of k with its upper end attached to ground at D. Let x represent the motion of the disk’s center of mass O (measured positively downward) with the spring being unstretched when x = 0. Assume that the cable does not slip on the disk and does not go slack at any time. a) Draw a free body diagram of the disk. b) Derive the single differential equation of motion (EOM) for the system in terms of the coordinate x and, at most, the following parameters: g , m , R and k . c) Let x st represent the value of x when the system is in static equilibrium. Recognizing that !! x = 0 when the system is in static equilibrium, determine the value of x st in terms of the system parameters from your EOM in b). d) Let z represent the motion of the system as measured from its static equilibrium case; that is, z ! x ! x st . Substitute this definition along with x st from c) into your EOM from b) to find the EOM in terms of z. How does this EOM differ from the one that you found in b)? k VERTICAL PLANE g R O C A x + m B D E
Vibrations Homework Problems ME 274 Problem VI-4 A guitar string is stretched between two supports (with the supports separated by distance of L ). The string has a mass/length of ! string ( slug/foot ) and is given a tension of T ( pounds ). It is known that the transverse motion of the center of the string, y(t), can be modeled by a simple spring-mass system in a horizontal plane provided that the following stiffness K and mass M are used for this system: K = 4 T L ( pound/foot ) and M = 0.405 m string , where m string is the true mass of the string ( slugs ). a) Derive the equation of motion (EOM) for the equivalent spring-mass system shown. Although you might be able to write down this EOM by inspection, please do not; it is good practice to derive the EOM each time. b)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 12/25/2011.

Page1 / 14

chap_VI_hwk_fall_2010 - Vibrations Homework Problems ME 274...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online