If \(x = 5 \mathrm {sin }\left(\pi t+ {\dfrac {\pi} 3}\right)~\text m\) represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively are:
1. \(5~\text m, 2~\text s\)
2. \(5~\text {cm}, 1~\text s\)
3. \(5~\text m, 1~\text s\)
4. \(5~\text {cm}, 2~\text s\)
Subtopic:  Simple Harmonic Motion |
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The \(x\text-t\) graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at \(t=2\) s is:
         
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. \(\dfrac{\pi^2}{16} ~\text{ms}^{-2}\)
Subtopic:  Simple Harmonic Motion |
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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. \(\pi ~\text{rad}\)
Subtopic:  Simple Harmonic Motion |
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The displacement of a particle executing simple harmonic motion is given by, \(y = A_{0} + A\sin \omega t+ B \cos\omega t.\)
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. \(\sqrt{A_{0}^{2}+\left( A + B \right)^{2}}\)
Subtopic:  Simple Harmonic Motion |
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The average velocity of a particle executing SHM in one complete vibration is:
1. zero
2. \(\dfrac{A \omega}{2}\)
3. \(A \omega\)
4. \(\dfrac{A \left(\omega\right)^{2}}{2}\)

Subtopic:  Simple Harmonic Motion |
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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

Subtopic:  Simple Harmonic Motion |
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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. \(\frac{\sqrt5}{\pi}\)

Subtopic:  Simple Harmonic Motion |
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A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then its time period of vibration will be:

1. \(\frac {\beta^2}{\alpha^2}\) 2. \(\frac {\beta}{\alpha}\)
3. \(\frac {\beta^2}{\alpha}\) 4. \(\frac {2\pi \beta}{\alpha}\)

Subtopic:  Simple Harmonic Motion |
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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 \(\frac{a+b}{2}\).
Subtopic:  Simple Harmonic Motion |
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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. \(2 \pi \sqrt{\dfrac{v_{1}^{2}-v_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}}\)
Subtopic:  Simple Harmonic Motion |
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