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In this assignment is based on two questions, one question is based on simple harmonic motion of inertias attached onto a torsion’s shaft, where the shaft acts as a torsion’s spring. The second question is based on portion of a cylindrical surface rocking on top of a fixed surface, that when it is rocked from side to side, what energy is applied and the natural frequency of oscillation. For question 1, the method that was used to attempt the question was to calculate the inertia values of the masses that are on the shaft, using the numbers of the student’s student numbers.
Once the inertia values are acquired, it is then calculated the torsion’s spring constants of the shaft at each section, using the torsion’s spring constant formula: k=GAL After determining the torsion’s spring constant, applying Newton’s second law into this concept, to find the forces acting on each section of the shaft. After determining the force equations for each section of the shaft, it is noticed that there leaves 4 force equations. The four force equations are then inputted into a ex. matrix to then find the determinate, which would therefore evaluate the natural frequency equations.
Using the maple software to assist in finding the determinate, leaves the following natural frequency equation. 3603572wN8- solving the natural frequency equation leaves the natural frequency values: NON=81. 90756695 radii WIN=178. 3540130 radii NON=240. 7286121 radii These values are then compared to Holder’s table to determine if these values are correct and to find the natural modes. Its is found that when these values are entered into the holder’s table, the column is -0. 000619, this is really close to O, and this also to determines the mode shape, from the 14).
These mode shape values are then plotted to a graph, which is shown below in figures 2 and 3. For question 2 of the assignment, has to determine the rocking motion of the arc that is on top the fixed mass. When calculating the new inertia of the rocking mass, parallel axis theorem is used to determine the new inertia, GIG=marry-Sinatra When determining the energy equations of the system, the consideration of the potential and kinetic energy equations are needed. As there is rocking motion of the mass and the change in centered position of the mass.
It is determined that for the intent energy equation of the system, it is split up into the translational and rotational component.