Question

7. The displacement of a solid body is to be monitored by a transducer (second-order system) with signal output displayed on a recorder (second-order system). The displacement is expected to vary sinusoidally between 2 and 5mm at a rate of 85Hz. Select appropriate design specifications for the measurement system for no more than 5% dynamic error (i.e., specify an acceptable range for natural frequency and damping ratio for each device).

Answer 1

ANSWER:

Given that:

7.

The displacement of a solid body is to be monitored by a transducer (second-order system) with signal output displayed on a recorder (second-order system).

The displacement is expected to vary sinusoidally between 2 and 5mm at a rate of 85Hz.

input sinusoidal signal range

if it is in form of -A to A then we can say A sinwt sut as it is not symmetrical about origin it will be in form of

input signal R(t) = 3.5+1.5 sin wt

in general for second order (or) coupled systems

for second order systems.

dynamic error

as error

select any two values for M ₁ M ₂ in this range

M ₁ = 0.98 , M ₂ = 1.02

Now for M ₁ = 0.98

from quation (1)

M₂ = 1.02

This is one apprache to this problem, the different assumption may give different solution.