In a certain dynamic measurement application, the input - output relationship is
ID: 2995906 • Letter: I
Question
In a certain dynamic measurement application, the input - output relationship is given by y = 1 + (1 + x)e-x. With what absolute uncertainty must 'x' be determined in order to yield an uncertainty of plusminus 0.2% for 4y' at a value of x = 6. The general differential equation tor an n,h order measuring instrument can be written as: Using this equation, write the differential equations for first and second-order measuring instruments. Give one example each for a first and second order instrument.Explanation / Answer
3.
y = 1+ (1+x ) exp (-x)
dy/dx = exp (-x) - (1+x) exp (-x)
assuming , dy/dx = delta y / delta x ,
given at x = 6 , delta y = 0.002 and we need to find delta x .
so,
0.002/delta x = exp (-6) - (1+6) exp (-6)
delta x =-0.1345
absolute uncertainty in x (is +ve/-ve) = 13.45 %
4. for first order
a1 dx/dt + a0 = F(t)
for second order .
a2 d2x/dt^2 + a1 dx/dt + a0 = F(t)