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Mechanical Measurements HW1 Solution

# Mechanical Measurements HW1 Solution - PROBLEM 1.17 KNOWN...

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PROBLEM 1.17 KNOWN: Data of form y = ax b . FIND: a and b; K SOLUTION The data are plotted below. If y = ax b , then in log-log format the data will take the linear form log y = log a + b log x A more or less linear curve results with this data. From the plot, the curve fit found is log y = -0.23 + 2x This implies that y = 0.59x 2 so that a = 0.59 and b = 2. The static sensitivity is found by the slope dy/dx at each value of x. x [m] K(x 1 ) = dy/dx x1 [cm/m] 0.5 0.54 2.0 2.16 5.0 5.40 10.0 10.80 COMMENT An aspect of this problem is to draw attention to the fact that many measurement systems may have a static sensitivity that is dependent on input value. The operating principle of many systems will determine how K behaves. p1.17 0.1 1 10 100 0.1 1 10 X [m] y [cm]

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PROBLEM 3.4 KNOWN: System model equation K = 1 unit/unit F(t) = 100U(t) y(0) = 75 units FIND: y(t) SOLUTION (a) The solution to the system model was shown to be given by the general form, y(t) = y + (y(0) - y )e -t/ τ where here, y(0) = 75 units y = 100 units τ = 0.5 s (determined from the system equation) then, y(t) = 100 + (75 - 100) e -t/0.5 units Alternatively, by direct solution and with y(0) = 75 units,
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Mechanical Measurements HW1 Solution - PROBLEM 1.17 KNOWN...

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