JEE Mains · Physics · STD 11 - 13. oscillations
Match List-I with List-II.
| List-I | List-II |
|---|---|
| A. \(\sin^2 \omega t\) | I. Periodic with time period \(T = \dfrac{\pi}{\omega}\) but not simple harmonic motion (SHM) |
| B. \(\sin^3(2\omega t)\) | II. Periodic with time period \(T = \dfrac{2\pi}{\omega}\) but Not SHM |
| C. \(\sin(\omega t) + \cos(\pi \omega t)\) | III. Periodic with time period \(T = \dfrac{\pi}{\omega}\) and SHM |
| D. \(\cos\omega t + \cos 2\omega t\) | 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
Answer & Solution
Correct Answer
(A) A-III, B-I, C-IV, D-II
Step-by-step Solution
Detailed explanation
For A: \(y = \sin^2 \omega t = \dfrac{1 - \cos 2\omega t}{2} = \dfrac{1}{2} - \dfrac{1}{2} \cos 2\omega t\) This represents simple harmonic motion (SHM) about the mean position \(y = \dfrac{1}{2}\) with an angular frequency of \(2\omega\). The time period is…
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