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Friday, 9 October

JEE Main 2024 · PhysicsNumerical answerNumerical valueMediumMulti-step

JEE Main 31 January 2024, Shift 2, Physics Q54

Question 54 of 90 in this shift, Physics question 24 of 30, Section B.

The time period of simple harmonic motion of mass MM in the given figure is παM5k\pi\sqrt{\frac{\alpha M}{5k}}, where the value of α\alpha is __________.

The figure, in words

Spring system hung from the ceiling, all springs of force constant k: the left spring connects the ceiling directly to mass M; the middle and right springs hang in parallel from the ceiling and join at a lower point, from which a fourth spring k connects down to mass M.

Official answer

12

NTA final key.

Chapter
Oscillations
Topic
SHM Equations
Idea tested
Springs in Series

Same topic in other shifts

All SHM Equations questions
  1. 2 Apr 2026, Shift 2 · Q45The equation of motion of a particle is given by x=asin⁡(50t+π3)x = a\sin\left(50t + \frac{\pi}{3}\right) cm. The particle will come to rest at time…MediumSingle correct
  2. 4 Apr 2026, Shift 1 · Q48The velocity of a particle executing simple harmonic motion along xx-axis is described as v2=50−x2v^2=50-x^2, where xx represents…EasyNumerical value
  3. 5 Apr 2026, Shift 2 · Q35Match List - I with List - II. List - I A. sin⁡2ωt\sin^2\omega t B. sin⁡3(2ωt)\sin^3(2\omega t) C. sin⁡(ωt)+cos⁡(πωt)\sin(\omega t)+\cos(\pi\omega t) D.…HardMatch the list
  4. 6 Apr 2026, Shift 1 · Q37A particle is executing simple harmonic motion. Its amplitude is AA and time period is 5 sec. The time required by it to move from x=Ax=A…EasySingle correct
  5. 8 Apr 2026, Shift 2 · Q37The frequency of oscillation of a mass mm suspended by a spring is v1v_1. If the length of the spring is cut to half, the same mass…EasySingle correct
  6. 2 Apr 2025, Shift 1 · Q33A particle is subjected to two simple harmonic motions as : x1=7sin⁡5tx_1=\sqrt{7}\sin5t cm and x2=27sin⁡(5t+π3)x_2=2\sqrt{7}\sin\left(5t+\frac{\pi}{3}\right)…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.