Exam#1
ME5655
Advanced Dynamics and Vibration
Problem1: ( 35 pt)
During the instant shown the frame. of the X-ray camera is rotating about the vertical axis at ωz = 5rad/s and ωz = 2rad/s2. Relative to the frame. the arm is rotating at ωrel = 2rad/s and ωrel = 1rad/s2. Determine the velocity and acceleration of the center of Camera at this instant. If the camera can be modeled as a rigid cylinder with radius of 0.1 m, height of 0.2 m and mass of 2 Kg , find the forces and moments are exerted at the camera supporting system. Assume point C is the center of the cylinder and supporting point is at the end of the cylinder. The entire cylinder is not shown in the Figure only half is shown.
Problem 2: (35 pt)
A thin ring is attached to a hinge as shown in the Figure. The ring is in the YZ plane. If the ring is disturbed from its equilibrium position in the YZ plane, write its equation of motion. For a small disturbance what is its frequency of oscillation ( natural frequency)
If the ring is disturbed from its equilibrium position and at the same time is being rotated about the Z axis with angular velocity of Ω, write again its equation of motion and identify all equilibrium positions and its stability. The ring radius is R, and its mass is m.
Problem 3(30 pt)
A square plate with mass M is pinned at one corner and it is attached by a string at the other corner as shown.
A ball with a mass m0 and velocity v0 is impacting plate at its mid length as shown. If duration of impact is 0.01 sec and ball is rebound with coefficient of restitution of 0.7,
a) What should be the ball velocity in order string rupture. a=10 cm, b=20 cm, M=1kg, m0=0.1 kg, Tension to break string =1000 N, g=10m/s2.
b) Write equation of motion of Plate after string is ruptured. What are the initial conditions?
c) How far the plate swing when stopped swinging.