Academia Aeternum
तमसो मा ज्योतिर्गमय
Wisdom · Knowledge · Eternity
Fifty multiple-choice questions drawn directly from 8 major competitive and board examinations spanning 25 years — IIT-JEE, NEET, CBSE, AIIMS, BITSAT, KVPY, and Olympiad. Every question is exam-tagged with its year of appearance.
Sourced from 8 exam bodies across 25 years of actual competitive and board papers. Each carries exam name and year.
Velocity at position x, acceleration direction, zero-crossing timing, and the defining condition F=−kx. The #1 topic across all 8 exam boards.
Total energy, KE at displacement x, energy when amplitude doubles, average KE over a full cycle. Especially dominant in JEE and AIIMS questions.
How time period and frequency change when mass, spring constant, or pendulum length is altered. Consistently tested since 1997.
Pendulum on Moon, on a hill, with doubled length. Spring constant doubling and mass replacement. Classic multi-step problems from JEE 2000–2017.
Phase difference between v and x (π/2), a and x (π). Graph shape identification for a–x, KE–x, PE–x. Favoured by NEET and CBSE boards.
SI unit of angular frequency, dimension of spring constant k, definition of initial phase. Recurring in CBSE and AIIMS from 2006–2015.
Of the 18 JEE questions, 7 involve energy — often paired with amplitude changes or position-specific substitution. The formula E=½mω²A² is the single most useful equation for this subset.
NEET questions lean towards conceptual pendulum scenarios — Moon, hill, doubled length — and definitional clarity. NEET rarely demands deep calculus derivations.
Nearly 4 of 9 CBSE questions cover unit identification, dimension, or graph-type discrimination — "unit of angular frequency", "shape of a–x graph" — steadily from 2006 to 2015.
BITSAT questions are numerically clean but use parameter-swap traps — doubling mass, halving k, replacing springs. Answer choices are arranged to catch the common directional error.
Maximum velocity (v=ωA), phase difference between a and x (π), and pendulum on Moon have appeared across IIT-JEE, NEET, and CBSE in multiple years.
Questions from 2013 onwards embed formulas in physical scenarios — spring on incline, pendulum in accelerating lift — rather than asking formula recall directly. Seen especially in JEE Main post-2013.
Set a 35-minute timer — that mirrors the per-section pace of JEE Main and NEET. Resist looking at the exam tag until after you have answered. Train your instinct, not your memory.
Once you answer, note which board set the question. Over time you will recognise the house style of each exam — JEE's layered framing vs NEET's direct phrasing vs CBSE's definition-first style.
Energy questions are the most frequent here. Before solving, ask: is this asking about E, KE, or PE? Confirm whether the amplitude or position is given. E ∝ A² catches most wrong answers.
After finishing, pull out all pendulum questions and revisit them together. The Moon, hill, elevator, and doubled-length variants are different faces of the same T = 2π√(L/g) logic and are best understood as a family.
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