A particle of mass 20g executes an SHM of amplitude 2.0cm. if the period of oscllation is 0.20s, waht is the mechanical energy expended in vibration

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A cantilever is driven in flexural vibration by an electrical coil mounted at its free end and moving in the field of a magnet. The coil has been so designed that its mass is sufficiently small that it may be neglected but unfortunately this resulted in the moment of inertia of the coil being by no means negligible. For the beam, Young's modulus is E, the density is p its length is I and the second moment of inertia is I. The moment of inertia of the coil about an axis through its centre of gravity (which coincides with the end of the beam) perpendicular to the plane of vibration is J. Determine the frequency equation for this system.

A mass of 5 kg is suspended on a spring and set oscillating. It is observed that the amplitude reduces to 5% of its initial value after 2 oscillations. It takes 0.5 seconds to complete two oscillations. Calculate the following: the damping ratio the natural frequncey the actual frequency  spring stiffness the critical damping coefficient the actual damping coefficient

THE SUBJECT IS VIBRATION ENGINEERING

Please do #11   section 3.6

A vehicle suspension system is idealized as a damper-spring-mass system, assuming natural frequency of 0.5Hz and damping coefficient 0.2. Suppose that the vehicle moves at speed V over a road with undulation similar to sinusoidal wave. Assume the undulation wavelength is 1000cm, and its height is 20cm. At what speed does the maximum amplitude of vibration occur, and what is the corresponding vibration amplitude?

A machine of mass 500kg is mounted through four mounting pads that exhibit linear elasticity and viscous damping. In mounting the machine each pad was observed to undergo a compression of 10mm. When the machine was given a small vertical deflection and let go it was found to execute free damped vibrations such that it made 80 oscillations in 18 seconds. For this system find: i.          The stiffness of each mounting                                                                                 ii.       The damping coefficient of each mounting                                                  iii.   The minimum number of oscillations and time it will take for the amplitude of vibration to be reduced to 2%

The natural frequency of a system is determined to be 15 Hz ignoring the effects of damping. Calculate the damped natural frequency of the system assuming a damping ratio of 0.7.

Given a SDOF of spring-mass-coulomb damping, with mas of 0.1kg, stiffness of 10N s/m and a damping force of 0.1N is excited by a harmonic force of 1N amplitude at 1hz. Assuming steady-state condition, calculate the amplitude of vibrationn of the mass. How long the vibration will continu if the excitation is removed?