By Matthew Hussey (auth.)

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Additional resources for Fundamentals of Mechanical Vibrations

Sample text

14 A waterfall has a steady flow of 105 m3 each 24 hour day and the height of the fall is 50 m. What is the power expended by gravity on the water? 15 A beam of rectangular cross-section 1 em x 2 em and length 2m is mounted as a cantilever. When a mass of 10 kg is hung from the free end the vertical deflection of the end is 5 em. Find the value of Young's modulus for the material of the beam. If the beam is mounted with its width, instead of its thickness, in the vertical direction what would the deflection be?

11 If a boat is observed to have a period of free vertical oscillations of 1 s and a horizontal cross-sectional area of keel of 10 m2 , what is its mass? 2 Hz. What is the spring constant of the coupling? 9). 13 In the first complete cycle of the vibration described by x = 5 cos -rrt + 10 sin-rrt, what are the maximum displacement and the maximum velocity and when is the velocity a maximum? 14 A spring of constant C1 hangs vertically downwards. Its lower end is attached to a spring of constant C2 whose lower end is attached to a mass M.

1. 5 Energy in the System The mechanical energy in the harmonic oscillator falls into the two categories, the kinetic energy of the mass Ek and the potential energy of the spring Ep. 5. The total mechanical energy in the system £ 1 is constant, that is, it is conserved but the form of that energy oscillates between kinetic and potential forms. The vanatwn of kinetic energy Ek and potential energy EP in the harmonic oscillator with time. 5 principle of conservation of mechanical energy. 21) wo for all positive integer values of n.