Question

A seismic instrument is constructed so that m = 0.45 kg and c cc  0.707 . A spring with k = 2.9 kN/m is used so that the instrument will be relatively insensitive to low-frequency signals for displacement measurements and relatively insensitive to high-frequency measurements. Calculate the value of the linear acceleration that will produce a relative displacement of 2.5 mm while the frequency is 20Hz.

Answer 1

The value of the linear acceleration that will produce a relative displacement of 2.5 mm while the frequency is 20 Hz is approximately 49.3 m/s².

Step-by-step explanation:

To calculate the linear acceleration that will produce a relative displacement of 2.5 mm while the frequency is 20 Hz, we can use the formula:

a = 4π²f²x

where a is the acceleration, f is the frequency, and x is the relative displacement.

Plugging in the given values:

a = 4π²(20 Hz)²(2.5 mm) = 500π² mm/s²

Converting the acceleration to meters:

a = 5π² m/s² ≈ 49.3 m/s²

Therefore, the value of the linear acceleration is approximately 49.3 m/s².