OpenStem

@openstem · Joined Jul 2026

7420 public items8 groups

Quiz10 questions

In a closed-loop control system, what is the error signal e(t)?

AThe output of the plantBThe difference between the setpoint and the measured output: e = r − yCThe integral of the control signalDThe noise from the sensor

Engineering

Engineering · L4 · Control Systems — 10 Q

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Quiz10 questions

A 500 N uniform beam of length 4 m is simply supported at both ends. What is each support reaction?

A500 N eachB250 N eachC125 N eachD1000 N each

Engineering

Engineering · L4 · Statics & Mechanics of Materials — 10 Q

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Quiz10 questions

An inverting op-amp amplifier has R_in = 10 kΩ and R_f = 100 kΩ. What is the voltage gain?

A−10B+10C−0.1D+0.1

Engineering

Engineering · L4 · Circuits, Signals & Fluid Mechanics — 10 Q

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Quiz7 questions

In the lift equation L = ½ρV²SC_L, what happens to lift if airspeed V doubles (all else constant)?

ALift doublesBLift stays the sameCLift quadruplesDLift halves

Engineering

Engineering · L4 · Aerodynamics — 7 Q

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Quiz7 questions

Which process family removes material from a solid blank to reach the final shape?

AAdditiveBSubtractiveCFormingDCasting

Engineering

Engineering · L4 · Manufacturing Processes & GD&T — 7 Q

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Quiz7 questions

For an ideal transformer with turns ratio a = N₁/N₂ = 10, if the primary voltage is 100 V, what is the secondary voltage?

A1000 VB100 VC10 VD0.1 V

Engineering

Engineering · L4 · Electrical Machines & Power Systems — 7 Q

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Quiz7 questions

An LTI system's output for any input x(t) can be found by:

AMultiplying x(t) directly by the impulse response h(t)BConvolving x(t) with the impulse response h(t)CAdding x(t) to h(t)DDifferentiating x(t) with respect to h(t)

Engineering

Engineering · L4 · Signals & Systems — 7 Q

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Quiz7 questions

The natural frequency of an undamped spring-mass system is:

Aωₙ = k/mBωₙ = √(k/m)Cωₙ = √(m/k)Dωₙ = m/k

Engineering

Engineering · L4 · Mechanical Vibrations — 7 Q

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Quiz3 questions

In the Galerkin FEM, the trial and test function spaces are:

ADifferent — trial functions are polynomials, test functions are Dirac deltasBChosen adaptively from the residualCIdentical finite-dimensional subspacesDInfinite-dimensional Sobolev spaces

Engineering

Engineering · L5 · Finite Element Method

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Quiz4 questions

The algebraic Riccati equation for LQR is:

AAᵀP + PA − PBR⁻¹BᵀP + Q = 0BAP + PAᵀ + PBR⁻¹BᵀP − Q = 0CAᵀP + PA + PBR⁻¹BᵀP + Q = 0DAᵀP − PA + PBR⁻¹BᵀP = Q

Engineering

Engineering · L5 · Optimal Control & Stability

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Quiz6 questions

The Kalman filter's predict step updates the covariance as:

APₖ⁻ = APₖ₋₁Aᵀ + Q, growing uncertainty by the process noiseBPₖ⁻ = (I − KH)Pₖ₋₁, always shrinking uncertaintyCPₖ⁻ = HPₖ₋₁Hᵀ + RDPₖ⁻ is unaffected by the predict step

Engineering

Engineering · L5 · Kalman Filtering & State Estimation — 6 Q

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Quiz7 questions

In MPC, after solving the finite-horizon optimization for u0, u1, ..., u_{N-1}, which control move is actually applied to the plant?

AOnly u0, the first move in the sequenceBThe entire sequence, open-loop, until the next horizonCThe average of all N movesDu_{N-1}, the last move in the sequence

Engineering

Engineering · L5 · Model Predictive Control — 7 Q

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Quiz6 questions

Forward kinematics for a serial manipulator:

AAlways has a unique solution given the joint variablesBCommonly has multiple solutions, like 'elbow up' vs 'elbow down'CCannot be computed for more than 3 jointsDRequires solving the equations of motion

Engineering

Engineering · L5 · Robot Kinematics & Dynamics — 6 Q

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Note~79 words · 1 min

Four steps engineers follow Failing the test isn't the end. It's the reason you built the thing: to find out what to change before it matters.

Engineering

Engineering · L1 · The Design Process: Ask, Imagine, Build, Test

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Note~169 words · 1 min

Everything is made of something A chair might be wood, a spoon metal, a bottle plastic, a shirt fabric. What something is made of is its material, and different materials behave in completely different ways. Four words engineers use A mater

Engineering

Engineering · L1 · What Are Materials?

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Note~231 words · 1 min

Push a square Build a square from four straws taped at the corners. Push sideways on the top corner and it leans right over into a slanted shape called a parallelogram. The straws never changed length. The CORNERS bent, like little hinges,

Engineering

Engineering · L1 · Strong Shapes: Triangles vs Squares

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Note~177 words · 1 min

Four parts Building it in order The bulb stays dark This happens to every builder. Work through the most likely cause first.

Engineering

Engineering · L1 · Build Your First Circuit

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Note~135 words · 1 min

Every tool has a job The right tool makes a job easier and safer. The wrong one makes it slow, messy, or dangerous. Safety rules

Engineering

Engineering · L1 · Picking the Right Tool, and Staying Safe

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Note~200 words · 1 min

A long trip through pipes Water starts at a tower or treatment plant, travels through a huge network of pipes buried under the streets, and finally arrives at your tap. Engineers design that whole network: where the pipes go, how big they a

Engineering

Engineering · L1 · Pipes & Water Flow

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Note~208 words · 1 min

Some materials carry heat fast Leave a metal spoon in a hot pot of soup and the handle is too hot to hold within a minute. Metal is a good heat conductor: heat races through it. Try a wooden spoon and the handle stays cool, however long it

Engineering

Engineering · L1 · Materials That Change With Heat

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Note~155 words · 1 min

Measure twice, cut once Engineers measure before they build so the parts fit together the way they planned. Two tools, two questions Why everyone needs the same units Two friends build a toy box. One measures the sides in centimetres with a

Engineering

Engineering · L1 · Measuring & Units

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Note~163 words · 1 min

Every invention fixes a problem Almost everything you use was invented by someone who noticed a problem and thought of a way round it. That's what engineers do: they think like problem-solvers. Thinking like an inventor Notice the loop back

Engineering

Engineering · L1 · Everyday Inventions & the Problems They Solve

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Note~205 words · 1 min

Why we build bridges A bridge lets people, cars and trains cross a gap (a river, a valley, a road) instead of going all the way round it. Engineers pick a shape that suits the gap. How each one holds the weight Spot the bridge

Engineering

Engineering · L1 · Bridges for Kids: Beam, Arch, and Suspension

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Note~232 words · 1 min

Why wide bases stand firm Stack blocks into a tall thin column and a light tap knocks it over. Start with a wide layer at the bottom and it takes a much bigger push. The pyramid shape A pyramid is wide at the bottom and narrow at the top. T

Engineering

Engineering · L1 · Towers & Stacking: Why Wide Bases Win

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Note~184 words · 1 min

A message with no wire Press a button on a remote and it sends an invisible signal through the air. A sensor on the TV catches it and the TV reacts. Every button sends its own code. Volume-up sends one, channel sends a different one, which

Engineering

Engineering · L1 · How Remote Controls Send Signals

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Note~172 words · 1 min

A motor turns electricity into spinning Give a motor power, from a battery or a wall plug, and its middle part spins round and round. That's the whole job. A fan is a motor plus blades The motor spins, the blades spin with it, and the blade

Engineering

Engineering · L1 · Motors: The Spinning Part Inside

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Note~192 words · 1 min

Why a metal boat floats Drop a lump of metal in water and it sinks. So why does an enormous metal ship float? Loading evenly Cargo has to be spread across both sides. Pile too much on one side and the boat leans, and a leaning boat can tip

Engineering

Engineering · L1 · Boats & Floating Cargo

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Note~204 words · 1 min

Clothes are little machines Every piece of clothing has a job. A raincoat keeps water out. A winter coat keeps warm air in. Sunglasses keep bright light off your eyes. Engineers pick a material to match each job. Layers trap warm air Waterp

Engineering

Engineering · L1 · Dressing for Weather

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Note~190 words · 1 min

Three properties, often confused Strong is not flexible Hard is not strong The bike helmet: two materials, two jobs The question an engineer actually asks Not "what's the best material?" but "what must this part survive, and which propertie

Engineering

Engineering · L2 · Material Properties: Strength, Flexibility, Hardness

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Note~248 words · 1 min

A frame made of triangles Why the triangle is the whole trick How the load travels Every member carries force along its own length. None of them bend, which is exactly why so little material is needed. Where trusses go Two common patterns

Engineering

Engineering · L2 · Trusses & Triangulation

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