Match List - I with List - II. List - I A. sin^2(omega t) B. sin^3(2omega t) C. sin(omega t) + cos(pi omega t) D. cos(omega t) + cos(2omega t) List - II I. Periodic with time period T = pi/omega but not simple harmonic motion (SHM) II. Periodic with time period T = 2pi/omega but Not SHM III. Periodic with time period T = pi/omega and SHM IV. Non-periodic Choose the correct answer from the options given below:

The correct answer is Option 1. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q35 – JEE-MAIN 2026

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Match List - I with List - II.

\begin{array}{lcl} 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 \end{array}

Choose the correct answer from the options given below:

Clue 1 of 3: Trigonometric Identities

Simplify the given functions using relevant trigonometric identities to identify their fundamental frequencies and periods.

🧠 Full Solution Path

Step 1: Analyze Function A:

\sin^{2} (ω t)

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Using the identity $\sin^{2} (x) = \frac{1 - \cos (2 x)}{2}$ , we can rewrite the function as:

\sin^{2} (ω t) = \frac{1 - \cos (2 ω t)}{2} = \frac{1}{2} - \frac{1}{2} \cos (2 ω t)

This represents a simple harmonic motion (SHM) about a mean position of $\frac{1}{2}$ with angular frequency $2 ω$ . The time period is $T = \frac{2 π}{2 ω} = \frac{π}{ω}$ . Thus, A matches with III.

Step 2: Analyze Functions B, C, D○ Expand

For B. $\sin^{3} (2 ω t)$ : Using $\sin^{3} (x) = \frac{3 \sin (x) - \sin (3 x)}{4}$ , we get $\frac{3}{4} \sin (2 ω t) - \frac{1}{4} \sin (6 ω t)$ . This is a superposition of two SHMs with periods $T_{1} = \frac{2 π}{2 ω} = \frac{π}{ω}$ and $T_{2} = \frac{2 π}{6 ω} = \frac{π}{3 ω}$ . The fundamental period is $L C M (\frac{π}{ω}, \frac{π}{3 ω}) = \frac{π}{ω}$ . It is not SHM. Thus, B matches with I.

For C. $\sin (ω t) + \cos (π ω t)$ : The periods are $T_{1} = \frac{2 π}{ω}$ and $T_{2} = \frac{2 π}{π ω} = \frac{2}{ω}$ . The ratio $\frac{T_{1}}{T_{2}} = \frac{2 π / ω}{2 / ω} = π$ , which is irrational. Therefore, the function is non-periodic. Thus, C matches with IV.

For D. $\cos (ω t) + \cos (2 ω t)$ : This is a superposition of two SHMs with periods $T_{1} = \frac{2 π}{ω}$ and $T_{2} = \frac{2 π}{2 ω} = \frac{π}{ω}$ . The fundamental period is $L C M (\frac{2 π}{ω}, \frac{π}{ω}) = \frac{2 π}{ω}$ . It is not SHM. Thus, D matches with II.

💡 Teacher's Secret Hint

Remember that a superposition of SHMs with different frequencies is periodic but not SHM.

Step 3: Final Matching and Option Selection○ Expand

Combining the matches:

A - III

B - I

C - IV

D - II

This combination corresponds to option 1.

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Physics Question 35 – JEE-MAIN 2026

Clue 1 of 3: Trigonometric Identities

🧠 Full Solution Path