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(a) Explain in a few sentences the difference between a natural frequency and a resonant frequency. Also clarify why for a specific system or component these frequencies may differ in value.
(b) Explain why accelerometers are generally used in NVH to measure the magnitude of vibrations, rather than velocity or displacement transducers. Also discuss the circumstances when it may be preferable to measure displacement or velocity.
(c) In the analysis of dynamic systems it is sometimes expedient to assume a viscous damping model and in other circumstances to assume a hysteretic damping model. Explain in your own words why this is the case. Do not supply an answer that you don't understand.
(d) It is a rule of modal analysis that every mode of vibration must be different. But for some components there may be natural frequencies that are theoretically identical in value. Explain how these repeated natural frequencies can arise.
program to find area under the curve y=f(x) between x=a and y=b , integrate y=f(x)between limits of a and b
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