KAIST Mechanical Engineering Grad Written Exam — Part 2: Set 2 (5 Problems, 2019)
📅 Following Set 1, this post covers Set 2 (the second 2-hour block, 5 problems) of the same day.
Previous post:
Q1 — Math: Eigenvalue / Eigenvector (3-variable ODE system)
A system of three linearly-combined linear differential equations: $$y_1'' = a y_1 + b y_2 + c y_3$$ $$y_2'' = d y_1 + e y_2 + f y_3$$ $$y_3'' = g y_1 + h y_2 + i y_3$$
Express in matrix form → set det(A - λI) = 0 to prove eigenvector existence → solve for λ and the corresponding eigenvectors.
⚠️ Know 3×3 determinant, inverse, and eigenvalue computation cold.
Additional note (from earlier years): Conservative fields have shown up. Cover vector calculus broadly — from path independence to Stokes' theorem — for safety.
Q2 — Solid Mechanics: Full Strength-Design Pipeline (Statics → Principal Stress → Safety)
Easier analysis than Set 1, but a long pipeline that ate time.
Standard 5-step strength design
1) Statics — Free-body diagram → all reaction forces
2) Section of interest — Shear force diagram + Moment diagram
3) Stress — Normal + Shear (Torsion + Bending + Tension/Compression combined)
4) Principal stress at max-stress point
(2D → Mohr's circle, 3D → eigenvectors for orientation)
5) Principal stress → Factor of safety
This problem: utility pole + wire preventing deflection. The wire is assumed to carry no moment. Had to back out tension from the wire's strain.
Side notes
- Beyond strength design, stability design (buckling) also worth knowing.
- Fatigue belongs to material-behavior territory.
Q3 — Dynamics: Rigid Body — Work & Energy
Two bars of length L fixed at a point, arranged in a T shape (⊥). No translation, rotation only. Released from a given position.
- (a) Mass moment of inertia
- (b) Maximum angular velocity
- (c) Highest position reachable (prove)
Same as Set 1 — Work & Energy.
Dynamics doesn't surprise. Pick the right approach (EoM / Work-Energy / Impulse-Momentum) for the problem.
Q4 — Thermodynamics: T-v Diagram / Properties
Simple-looking, but unforgiving if you don't know the concept.
[Problem] A vast lake (initial state 25°C, 1 atm) receives 1 kg of hot water at 100°C. What is the maximum extractable energy (work)?
Given: $h_{fg}$, $h_f$, $h_g$, $C$ (heat capacity).
Property mastery is key — T-v diagram, state changes, plus the exergy concept and you're fine.
Q5 — Fluid Mechanics: Couette Flow — Navier-Stokes Equation
The fluids finale — Navier-Stokes.
[Couette Flow] Two different fluids. One plate stationary, the other moving.
- Start from the Navier-Stokes equation (Cartesian, cylindrical)
- State assumptions (laminar, 1-D flow, continuum)
- Apply boundary conditions → derive exact solution
Navier-Stokes is the go-to. Memorize both Cartesian and cylindrical forms.
Three analysis approaches in fluid mechanics
| Analysis | Key tool |
|---|---|
| Control volume | Reynolds Transport Theorem |
| Finite differential | Navier-Stokes equation |
| Dimensional | Π theorem (Buckingham) |
Know the first two solidly. Boundary layer / drag coefficient show up sometimes.
Set 2 wrap-up
Difficulty: easier analysis than Set 1, but the pipelines are long → time pressure. Strength-design 5 steps and Navier-Stokes derivation + BC work are hand-cramping.
Study targets (Set 2 view): - Math: 3×3 eigenvalue + vector calculus broadly - Solid: full 5-step strength design — statics through safety - Dynamics: same as Set 1 — Work-Energy - Thermo: properties (T-v, h_fg, h_f, h_g) + exergy intuition - Fluid: Navier-Stokes (both Cart + Cyl), Couette / Poiseuille variations
Closing
I ended up failing the KAIST interview and going to a different program. If this helps someone preparing the same path, that's enough. Take care of yourself and good luck out there.
📦 Migrated from my own Korean blog (my own writing). Original: taehyuklee.tistory.com/9 · earlier Naver version: blog.naver.com/fish991/221822659934
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