Measurements, instrumentation and controls shares the smallest technical range of the outline with electricity and magnetism: 5–8 questions. It rewards a short list of ideas used precisely: what a sensor converts, how a signal is conditioned, how a physical system responds, and how much to trust the number.
Updated Oct 29, 2026 · Not affiliated with NCEES.
ExamFE Mechanical
questions on the exam5–8
worked problems here14
of 14 knowledge areas13
Checked
What the area covers
Four topics in the specification:
Sensors and transducers: strain gauges and bridges, thermocouples, RTDs and thermistors, pressure transducers, LVDTs, accelerometers, flow and speed sensors.
Control systems: feedback loops and block diagrams, open- and closed-loop behavior.
Dynamic system response: first- and second-order behavior of physical systems such as a sensor or a mass-spring-damper.
Measurement uncertainty: error propagation, accuracy, precision and significant figures.
14 instrumentation and controls problems
0 / 14 answered · 0 correct
Question 1 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
An engineer is evaluating the uncertainty of a pneumatic test rig. A digital pressure transducer used in the system specifies an accuracy bound of ±2.1% of the reading on its datasheet. If the transducer is currently measuring a steady absolute pressure of 150 kPa, what is the standard measurement uncertainty of this specific reading assuming a rectangular probability distribution?
Given
Transducer accuracy = ±2.1% of reading
Reading p = 150 kPa
Find
Standard uncertainty u (kPa)
Solution
a = 0.021 × 150 kPa = 3.15 kPa
u = a/√3 = 3.15/1.732 = 1.82 kPa
a/√6 is the standard uncertainty for a triangular distribution, not a rectangular one.
a/2 treats the datasheet limit as an expanded uncertainty with coverage factor 2 (normal distribution).
The bound is a = 0.021 × 150 = 3.15 kPa; a rectangular distribution gives u = a/√3 = 1.82 kPa.
This is the half-width of the accuracy bound itself, not a standard uncertainty.
Multiplying by √3 instead of dividing inflates the result; the bound is wider than the standard deviation.
Question 2 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
A linear pressure transducer has a sensitivity of 5 mV/psi, a range of 0–100 psi, and an output of 50 mV at zero pressure. If the output voltage is 250 mV, what is the measured pressure?
Given
Sensitivity S = 5 mV/psi
Zero output V0 = 50 mV at 0 psi
Range = 0–100 psi
Output voltage V = 250 mV
Find
Measured pressure p (psi)
Solution
p = (V − V0)/S = (250 − 50) mV/(5 mV/psi) = 40 psi
Subtracting the 50 mV zero offset leaves 200 mV, and 200 mV ÷ 5 mV/psi = 40 psi.
This divides the raw 250 mV by the sensitivity and ignores the 50 mV the transducer outputs at zero pressure.
Adding the offset instead of subtracting it moves the reading the wrong way.
Multiplying the net voltage by the sensitivity inverts the calibration; p = ΔV/S.
Question 3 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
In sensor fusion applications, several sensor outputs with different uncertainties are combined in a nonlinear model using a first-order Taylor series expansion. What is a key assumption made about the sensor uncertainties in this method?
Solution
uy2 ≈ Σ(∂f/∂xi)2ui2 (valid when ui is small enough that f is locally linear)
The method weights each uncertainty by its own sensitivity coefficient, so they need not be equal.
A first-order Taylor expansion drops higher-order terms, which is accurate only when each uncertainty is a small perturbation about the operating point.
First-order propagation combines variances and does not require a normal distribution.
The usual root-sum-square form assumes the inputs are uncorrelated; correlation requires extra covariance terms.
Question 4 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
An engineer measures axial strain on a structural member using a single active strain gauge (quarter-bridge configuration). The actual physical strain experienced by the member is 400 microstrain. However, the data acquisition software is mistakenly left in its default "full-bridge (4 active gauges)" setting. A standard full-bridge yields 4 times the sensitivity of a quarter-bridge for the same physical strain and gauge factor. What strain value (in microstrain) will the software incorrectly report?
Given
Actual strain ε = 400 microstrain
Actual configuration: quarter bridge (1 active gauge)
Multiplying by 4 reverses the effect: the software expects more signal per microstrain, so it reports less.
Doubling applies a half-bridge factor in the wrong direction; a setting that expects more output per microstrain under-reports, never over-reports.
This is the true strain; the wrong bridge setting changes the conversion factor, so the report is not correct.
This assumes a half bridge (2 active gauges) setting; the software was set for a full bridge.
Software set for a full bridge expects four times the output per microstrain, so it divides the quarter-bridge signal by 4: 400/4 = 100 µε.
Question 5 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
A temperature measurement system consists of a sensor, an amplifier, and a 12-bit analog-to-digital converter (ADC) with a full-scale range of 0 to 5.0 V. The sensor has a linear sensitivity of 10 mV/°C. The amplifier has a constant gain of 20. What is most nearly the fundamental detection threshold (smallest detectable change) of the temperature in engineering units?
Multiplying the LSB by the gain instead of dividing by it inflates the threshold 400-fold.
This ignores the amplifier: the LSB must be divided by the gain of 20 before converting to temperature.
This takes the sensitivity as 1 mV/°C; a tenfold unit slip in the sensor output.
Using 211 = 2048 counts halves the resolution; a 12-bit converter has 4096 levels.
1 LSB = 5.0 V/4096 = 1.22 mV at the ADC; referred back through the gain of 20 and 10 mV/°C, that is 1.22 mV/(0.2 V/°C) = 0.0061 °C.
Question 6 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
Which of the following best describes a first-order system's step response?
Solution
y(t) = K·A(1 − e−t/τ) (63.2% at t = τ, ≈ 98% at 4τ)
A first-order response starts with its steepest slope and then levels off; it is not a constant-slope ramp.
A first-order system reaches 63.2% of the step after one time constant and approaches the final value monotonically.
An instantaneous rise describes a zero-order (pure gain) system with no energy storage.
Overshoot and oscillation need two energy-storage elements, an underdamped second-order system.
Question 7 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
Which characteristic of a measurement system describes its ability to give the same output for the same input in repeated trials under identical conditions?
Solution
Repeatability = agreement of repeated readings (same input, same conditions); accuracy = agreement with the true value.
Linearity is how closely the input-output curve follows a straight line across the range.
Accuracy is closeness to the true value; a repeatable instrument can still be consistently off.
Resolution is the smallest change in input the system can detect.
Repeatability is the closeness of successive readings of the same input under the same conditions.
Question 8 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
Piezoelectric sensors are frequently used for high-frequency dynamic measurements. What factor is most critical in ensuring accurate and reliable measurements with such sensors?
Solution
Piezoelectric sensor: q = d·F, very high output impedance → charge amplifier or high-impedance voltage follower; low-frequency limit set by the RC time constant.
Excessive gain causes clipping and adds noise; the issue is the input impedance, not more gain.
Low mass helps an accelerometer avoid loading a light structure, but it does not address the charge-leakage problem common to all piezoelectric sensors.
Sampling rate matters for capturing high frequencies, but it cannot recover a signal degraded by loading at the sensor.
A piezoelectric element produces charge with a very high source impedance; without a charge amplifier or high-impedance input, the signal leaks away and low frequencies are lost.
Question 9 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
An analog-to-digital converter samples a pressure transducer signal at a sampling rate of 1000 Hz. The signal is contaminated by high-frequency electrical noise at 2750 Hz. If no anti-aliasing filter is used, at what frequency will this noise appear in the sampled digital signal?
Given
Sampling rate fs = 1000 Hz
Noise frequency f = 2750 Hz
Find
Apparent (aliased) frequency (Hz)
Solution
falias = |f − N·fs| with N chosen to land in 0…fs/2
falias = |2750 − 3 × 1000| = 250 Hz
2750 Hz lies 250 Hz from 3 × 1000 Hz, so it folds to |2750 − 3000| = 250 Hz, inside the 0–500 Hz band.
500 Hz is the Nyquist frequency, the upper edge of the band; an alias lands at a specific folded frequency, not at the limit.
2750 − 2 × 1000 = 750 Hz is above the 500 Hz Nyquist limit, so it folds again to 250 Hz.
Subtracting one sampling frequency is not enough; the apparent frequency must lie between 0 and fs/2.
Subtracting half the sampling rate does not fold the frequency; aliasing works in multiples of fs.
Question 10 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
A quarter-bridge strain gauge circuit measures strain ε. The linearized bridge output is ΔVout = (Vexc/4)·GF·ε. The excitation voltage is Vexc = 10.00 V with a standard uncertainty of 0.05 V, and the gauge factor is GF = 2.00 with a standard uncertainty of 0.02. If the measured strain is ε = 0.00100, what is most nearly the combined standard uncertainty of the output voltage?
This is only the contribution from the excitation voltage; the gauge-factor term is twice as large.
This is only the gauge-factor contribution; the excitation uncertainty adds in quadrature.
∂V/∂Vexc·u = 0.0005 × 0.05 V = 0.025 mV and ∂V/∂GF·u = 0.0025 V × 0.02 = 0.050 mV; their root-sum-square is 0.0559 mV.
Adding the two contributions linearly overstates the combined uncertainty of independent inputs.
This doubles the root-sum-square result, as for an expanded uncertainty with k = 2; the question asks for the standard uncertainty.
Question 11 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
What is the primary purpose of a low-pass filter in a measurement system?
Solution
Low-pass filter: |H| ≈ 1 below fc, rolls off above it; used for noise reduction and anti-aliasing.
A passive filter has no gain; amplification is a separate stage.
A low-pass filter passes the slow measurement signal and attenuates content above its cutoff, including noise and frequencies that would alias.
Removing a DC offset takes a high-pass filter or offset correction; a low-pass filter passes DC.
Sensitivity is the output per unit input of the sensor chain; filtering does not change it.
Question 12 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
An analog signal with an RMS amplitude of 2.0 V is conditioned by an amplifier with a bandwidth of 10 kHz and sampled by an ADC. The sensor and amplifier produce a combined white noise spectral density of 150 μV/√(Hz) at the ADC input. The ADC has a quantization step size (LSB) of 0.0346 V. What is most nearly the total signal-to-noise ratio (SNR) in decibels at the sampled output?
This counts only the thermal noise and leaves out quantization noise.
This counts only the quantization noise and leaves out the 15 mV thermal noise.
Question 13 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
Which of the following sensors would be most appropriate for measuring angular velocity of a rotating shaft?
Solution
Angular velocity: tachometer or encoder (pulses per revolution × count rate).
A strain gauge measures surface strain; on a shaft it can give torque, not speed.
Piezoelectric sensors respond to dynamic force, pressure or acceleration, not to steady rotational speed.
A thermocouple measures temperature.
A tachometer (magnetic pickup, optical encoder or DC tach generator) gives an output proportional to shaft speed.
Question 14 of 14 · Measurements, Instrumentation, and Controls · 5–8 items
A type K thermocouple produces 2.00 mV while its reference junction sits at 25 °C. Treating its sensitivity as a constant 0.041 mV/°C over this range, what is the temperature of the measuring junction?
Subtracting the 25 °C reference instead of adding it puts the hot junction below the reference, but a positive emf means it is warmer.
48.8 °C is only the difference between the junctions; the reference junction is at 25 °C, not 0 °C.
The emf reflects the difference between the junctions: ΔT = 2.00/0.041 = 48.8 °C above the 25 °C reference, so T = 73.8 °C.
This adds the reference temperature twice.
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Common traps
Checked against the instrumentation, measurement and control material of the FE Reference Handbook and Figliola and Beasley's Theory and Design for Mechanical Measurements:
The thermocouple measures a difference. Its voltage depends on the temperature difference between the measuring junction and the reference junction. Using the table without the reference-junction correction shifts every reading.
RTD and thermistor are not twins. A platinum RTD is close to linear with a positive coefficient; a thermistor is strongly nonlinear and usually has a negative one.
Range is not span. A transducer rated −50 to +150 kPa has a span of 200 kPa. Accuracy quoted as a percent of full scale applies to the span or the full-scale value, not to the reading.
Closed loop is G/(1 + GH) for negative feedback. Sign errors at the summing junction flip the denominator. Reduce block diagrams one loop at a time.
Significant figures follow the weakest input. The Units and Conversion Factors chapter of the Handbook gives the rules; an answer with more digits than the data is not more accurate.
Half and full bridges cancel temperature
A single active gauge also responds to temperature. Placing a dummy or second active gauge in an adjacent arm of the bridge cancels the thermal output, which is why real installations rarely use a lone gauge.
Instrumentation and its neighbors
The second-order response here is the same equation as free vibration in dynamics, and a temperature sensor's first-order lag is the lumped-capacitance model from heat transfer. Statistics behind uncertainty, such as standard deviation and confidence intervals, are in the shared probability and statistics section.
Is this the same as the controls section on the electrical exam?
No. The mechanical outline asks about sensors, physical systems and uncertainty. Transfer-function analysis in depth belongs to the electrical and computer outline.
How many controls questions are on the FE Mechanical exam?
5–8 for measurements, instrumentation and controls together, the same range as electricity and magnetism.
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