• (a) The casing of a compressor is executing sinusoidal vibrations with a displacement amplitude of 10⁻⁴ m and a frequency of 500 Hz. Calculate the amplitude of the acceleration of the casing in units of g (g = 9.81 m s−2 ).

  (b) A piezoelectric crystal accelerometer has a steady-state sensitivity of 2.0 pC/g, a natural frequency of 20 kHz, a damping ratio of 0.1 and a capacitance of 100 pF. It is connected to an oscilloscope (a resistive load of 10 MΩ) by a cable of capacitance 100 pF.

  (i) Without performing detailed calculations, sketch magnitude and phase frequency response characteristics for the accelerometer. Using these characteristics:

  (ii) Estimate the amplitude of the voltage measured by the oscilloscope when the accelerometer is mounted on the casing described in (a).

  (iii) Explain why this system is unsuitable for measuring vibrations at 20 Hz. How should the system be modified to make these measurements possible?