Q. No.| (A) | parabolic path |
| (B) | elliptical path |
| (C) | periodic motion |
| (D) | simple harmonic motion |
Choose the correct answer from the options given below:
| 1. | (B), (C), and (D) only |
| 2. | (A), (B), and (C) only |
| 3. | (A), (C), and (D) only |
| 4. | (C) and (D) only |
| 1. | \(e^{-\omega t} \) | 2. | \(\text{sin}\omega t\) |
| 3. | \(\text{sin}\omega t+\text{cos}\omega t\) | 4. | \(\text{sin}(\omega t+\pi/4) \) |
| 1. | \(e^{\omega t}\) | 2. | \(\text{log}_e(\omega t)\) |
| 3. | \(\text{sin}\omega t+ \text{cos}\omega t\) | 4. | \(e^{-\omega t}\) |
| 1. | circle |
| 2. | hyperbola |
| 3. | ellipse |
| 4. | a straight line passing through the origin |
| 1. | \(5~\text m, 2~\text s\) | 2. | \(5~\text {cm}, 1~\text s\) |
| 3. | \(5~\text m, 1~\text s\) | 4. | \(5~\text {cm}, 2~\text s\) |
| 1. | \(-\dfrac{\pi^2}{16} ~\text{ms}^{-2}\) | 2. | \(\dfrac{\pi^2}{8}~ \text{ms}^{-2}\) |
| 3. | \(-\dfrac{\pi^2}{8} ~\text{ms}^{-2}\) | 4. | \(\dfrac{\pi^2}{16} ~\text{ms}^{-2}\) |
The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:
1. \(\dfrac{3\pi}{2}\text{rad}\)
2. \(\dfrac{\pi}{2}\text{rad}\)
3. zero
4. \(\pi ~\text{rad}\)
Then the amplitude of its oscillation is given by:
1. \(A + B\)
2. \(A_{0}+\sqrt{A^{2} + B^{2}} \)
3. \(\sqrt{A^{2} + B^{2}}\)
4. \(\sqrt{A_{0}^{2}+\left( A + B \right)^{2}}\)
The average velocity of a particle executing SHM in one complete vibration is:
1. zero
2. \(\dfrac{A \omega}{2}\)
3. \(A \omega\)
4. \(\dfrac{A \left(\omega\right)^{2}}{2}\)
A particle executes linear simple harmonic motion with amplitude of \(3~\text{cm}\). When the particle is at \(2~\text{cm}\) from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:
1. \(\dfrac{\sqrt5}{2\pi}\)
2. \(\dfrac{4\pi}{\sqrt5}\)
3. \(\dfrac{4\pi}{\sqrt3}\)
4. \(\dfrac{\sqrt5}{\pi}\)
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