Q. No.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. \(\dfrac{A \left(\omega\right)^{2}}{2}\)
The distance covered by a particle undergoing SHM in one time period is: (amplitude = A)
1. zero
2. A
3. 2 A
4. 4 A
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. \(\frac{\sqrt5}{2\pi}\)
2. \(\frac{4\pi}{\sqrt5}\)
3. \(\frac{4\pi}{\sqrt3}\)
4. \(\frac{\sqrt5}{\pi}\)
A particle is executing a simple harmonic motion. Its maximum acceleration is and maximum velocity is . Then its time period of vibration will be:
| 1. | \(\frac {\beta^2}{\alpha^2}\) | 2. | \(\frac {\beta}{\alpha}\) |
| 3. | \(\frac {\beta^2}{\alpha}\) | 4. | \(\frac {2\pi \beta}{\alpha}\) |
When two displacements are represented by \(y_1 = a \text{sin}(\omega t)\) and \(y_2 = b\text{cos}(\omega t)\) are superimposed, then the motion is:
| 1. | not simple harmonic. |
| 2. | simple harmonic with amplitude \(\frac{a}{b}\). |
| 3. | simple harmonic with amplitude \(\sqrt{a^2+b^{2}}.\) |
| 4. | simple harmonic with amplitude \(\frac{a+b}{2}\). |
A particle is executing SHM along a straight line. Its velocities at distances \(x_1\) and \(x_2\) from the mean position are \(v_1\) and \(v_2\), respectively. Its time period is:
| 1. | \(2 \pi \sqrt{\dfrac{x_{1}^{2}+x_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}}~\) | 2. | \(2 \pi \sqrt{\dfrac{{x}_{2}^{2}-{x}_{1}^{2}}{{v}_{1}^{2}-{v}_{2}^{2}}}\) |
| 3. | \(2 \pi \sqrt{\dfrac{v_{1}^{2}+v_{2}^{2}}{x_{1}^{2}+x_{2}^{2}}}\) | 4. | \(2 \pi \sqrt{\dfrac{v_{1}^{2}-v_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}}\) |
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