A LVDT output is recorded by a self-balancing potentiometric recorder having its natural frequency of 10Hz and damping ratio of 0.707. The LVDT is excited by 10V at 50Hz power supply. Estimate the maximum frequency of the displacement signal that can be recorded with an error of + 2%.

The question is asking for the maximum frequency of the displacement signal that can be recorded with an error of + 2%. This involves understanding the characteristics of the self-balancing potentiometric recorder and the LVDT (Linear Variable Differential Transformer).

The natural frequency (ωn) of the recorder is given as 10Hz and the damping ratio (ζ) is 0.707.

The frequency response of a second order system like this can be described by the following equation:

|G(jω)| = 1 / sqrt((1 - (ω/ωn)^2)^2 + (2ζω/ωn)^2)

Where:

• |G(jω)| is the magnitude of the frequency response
• ω is the frequency of the input signal
• ωn is the natural frequency
• ζ is the damping ratio

We want to find the maximum frequency (ω) that can be recorded with an error of + 2%. This means that the magnitude of the frequency response |G(jω)| should be 0.98 (since 1 - 0.02 = 0.98).

So, we need to solve the following equation for ω:

0.98 = 1 / sqrt((1 - (ω/10)^2)^2 + (20.707ω/10)^2)

This is a non-linear equation in ω and can be solved using numerical methods such as the Newton-Raphson method or by using software tools that can solve non-linear equations.

Once you solve this equation, you will get the value of ω which is the maximum frequency of the displacement signal that can be recorded with an error of + 2%.