Question 6.P.7: A seismic instrument designed to measure vertical accelerati...

Dynamics of Structures

A seismic instrument designed to measure vertical acceleration consists of a light beam $AB$ pivoted at $A$ through a torsional spring of constant $20Nm$ (Fig. P6.7). A small body of mass $0.6 kg$ is fixed to the beam at end $B$ and a viscous damper is attached at $C$ . The pointer $BED$ , pivoted to the $0.6 kg$ mass at $B$ and to the instrument casing at $E$ , moves over the scale at $D$ as shown in the figure. The viscous damper is adjusted to provide a damping of $0.7$ times the critical. Obtain the undamped natural frequency of the instrument and the damping coefficient of the viscous damper. The instrument is calibrated to read the support acceleration correctly at an input frequency of $1 Hz$ . Obtain the calibration factor. If the support acceleration is $3 m/s²$ at a frequency of $5 Hz$ what will be the instrument reading and what is the percentage error?

P6.7

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