#1 A mass measurement system behaves as a second-order system (consisting of a mass = 50g,...

#1 A mass measurement system behaves as a second-order system (consisting of a mass = 50g, a spring, and a viscous damping element). To determine the damping the ratio, the system was exposed to a step input and decaying oscillating amplitude of the system output was measured. Results of these measurements showed that the damping ratio = 0.7 and the ringing frequency f_d =389 Hz. Calculate the following and report results using 3 significant digits minimum:

The natural frequency, in Hz

The spring constant, in kN/m

Logarithmic decrement ln(x₁/x_n)

The period of oscillation when the system is exposed to a step input, in milliseconds

The dynamic error, ?, at 450 Hz in % (include the sign of the error)

The phase and time delay between input and output for sinusoidal inputs of 450 Hz in rad and milliseconds, respectively

Can we use this system to measure mass in outer space? How? Use a diagram to explain.

Expert Solution

samet mamat answered 2 years ago

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