JEE Main 2026 Apr 5 Shift 2, Physics Q10: Simple Harmonic Motion And Oscillation

JEE Main2026Apr 5, Shift 2Physics

Match List-I with List-II.

List-I	List-II
A. $sin^{2} ω t$	I. Periodic with time period $T = \frac{π}{ω}$ but not simple harmonic motion (SHM)
B. $sin^{3} (2 ω t)$	II. Periodic with time period $T = \frac{2 π}{ω}$ but not SHM
C. $sin (ω t) + cos (π ω t)$	III. Periodic with time period $T = \frac{π}{ω}$ and SHM
D. $cos ω t + cos 2 ω t$	IV. Non-periodic

Choose the correct answer from the options given below.

A
A-III, B-I, C-IV, D-II
B
A-II, B-I, C-III, D-IV
C
A-III, B-II, C-IV, D-I
D
A-II, B-I, C-IV, D-III

Solution

A. $sin^{2} ω t = \frac{1}{2} - \frac{1}{2} cos 2 ω t$ is sinusoidal in $2 ω t$ , hence SHM about the mean value $1/2$ , with period $π / ω$ . $\Rightarrow$ III.

B. $sin^{3} (2 ω t) = \frac{3}{4} sin (2 ω t) - \frac{1}{4} sin (6 ω t)$ . Common period $= π / ω$ , but it is a sum of two harmonics so not SHM. $\Rightarrow$ I.

C. $sin (ω t) + cos (π ω t)$ : the ratio of the two angular frequencies is irrational ( $π$ ), so no common period exists. $\Rightarrow$ IV (non-periodic).

D. $cos ω t + cos 2 ω t$ has common period $2 π / ω$ and is not SHM (sum of distinct harmonics). $\Rightarrow$ II.

$∴$ A $\to$ III, B $\to$ I, C $\to$ IV, D $\to$ II.

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JEE Main 2026 Apr 5 Shift 2, Physics Q10: Simple Harmonic Motion And Oscillation

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