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Match List-I with List-II.
List-I: (A) sin²(ω t) (B) sin³(2ω t) (C) sin(ω t)+cos(πω t) (D) cos ω t+cos 2ω t
List-II: (I) Periodic with time period T=π/ω but not simple harmonic motion (SHM) (II) Periodic with time period T=(2π)/ω but not SHM (III) Periodic with time period T=π/ω and SHM (IV) Non-periodic

Asked in JEE Main 5th April 2nd Shift 2026 · Identifying SHM

• (1) A-III, B-I, C-IV, D-II
• (2) A-II, B-I, C-III, D-IV
• (3) A-III, B-II, C-IV, D-I
• (4) A-II, B-I, C-IV, D-III

Step-by-step solution

Why the other options are wrong

• (2) Gives sin²ω t the period 2π/ω of sin ω t instead of the period of the cos 2ω t it really contains, and calls the incommensurate sum (C) simple harmonic.
• (3) Swaps B and D. The slowest term in sin³ 2ω t is sin 2ω t, so its period is π/ω, not 2π/ω.
• (4) Repeats the period slip on A and then calls cos ω t+cos 2ω t simple harmonic, although it contains two different frequencies.

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