Academia Aeternum
तमसो मा ज्योतिर्गमय
Wisdom · Knowledge · Eternity
A curated bank of 50 multiple-choice questions spanning NCERT fundamentals to JEE Advanced — with full topic coverage, difficulty progression, and previous year exam questions from IIT-JEE, NEET, BITSAT, KVPY, and more.
KE, PE, total energy, energy at x=A/2, average energy over cycle — single most tested cluster in this set.
F=−kx condition, restoring force, conservative nature — appears at every difficulty level from Q1 to Q50.
Angular frequency, time period, frequency — their mutual relations and dependence on system parameters like m and k.
Velocity, acceleration, displacement — maxima, minima, and behaviour at mean vs. extreme positions.
T=2π√(L/g), effect of g, seconds pendulum, pendulum on Moon — exam favourites recurring across 25+ years of JEE/NEET.
T=2π√(m/k), dimension of spring constant, effect of doubling m or k — critical for JEE Moderate and above.
For every v, a, or energy question — first identify whether the particle is at mean, extreme, or x=A/2. This resolves 80% of options instantly.
a–x graph is a straight line with negative slope (not a curve). KE–x and PE–x are parabolas. These are frequently distorted in answer options.
Since E = ½mω²A², doubling amplitude gives 4× energy, not 2×. This appears in Q7, Q11, and Q40 — three differently worded versions of the same rule.
v leads x by π/2. a leads v by π/2. So a is π ahead of x — anti-phase. Three questions (Q14, Q32, Q44) directly test this chain.
On Moon or a hill: g decreases → T increases → pendulum clock runs slow. Both give the same directional change — a deliberate trap in Q36.
When kinetic energy equals potential energy, displacement is A/√2 ≈ 0.707A. Q13 (NCERT) and Q39 (JEE Advanced) frame the same result differently.
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