By Matthew Hussey (auth.)
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Extra resources for Fundamentals of Mechanical Vibrations
Example text
A graph of L versus T 2 is a straight line with slope g/4-rr 2 from which g is found. (b) Vertical Spring Oscillator A hanging helical spring of constant C with a mass M attached to the bottom constitutes a harmonic oscillator with period T = 2-rrY(M/C), if the mass of the spring can be neglected relative to M. Since by measuring the time for a large number of oscillations, T can be determined accurately, this experiment can be used to measure any one of the two quantities M or C, if the other one is known.
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. 15 A steel beam, three-point loaded, is 2 mm thick, 2 em wide and 2m long. 2 x 10 12 N/m2 • A spring of constant 10 N/m hangs from the mid-point of the beam and a mass of 40 kg is attached to the lower end of this spring.
35. In this case the loss of potential energy in falling the distance d is equal to the gain of kinetic energy. The total mechanical energy is said to be conserved. This is an elementary example of the principle of conservation of mechanical energy. 13 A conventional force F versus deflection x graph for a spring, showing the work done (the cross-hatched area) in stretching the spring from x to x + dx. Work must be done in order to deform a spring and therefore energy may be stored in a spring.