Q. No.The average velocity of a particle executing SHM in one complete vibration is:
1. zero
2. \(\dfrac{A \omega}{2}\)
3. \(A \omega\)
4. \(\dfrac{A \left(\omega\right)^{2}}{2}\)
1. zero
2. \(\dfrac{A \omega}{2}\)
3. \(A \omega\)
4. \(\dfrac{A \left(\omega\right)^{2}}{2}\)
The radius of the circle, the period of revolution, initial position and direction of revolution are indicated in the figure.
The \(y\)-projection of the radius vector of rotating particle \(P\) will be:
| 1. | \(y(t)=3 \cos \left(\dfrac{\pi \mathrm{t}}{2}\right)\), where \(y\) in m |
| 2. | \(y(t)=-3 \cos 2 \pi t\) , where \(y\) in m |
| 3. | \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in m |
| 4. | \(y(t)=3 \cos \left(\dfrac{3 \pi \mathrm{t}}{2}\right) \), where \(y\) in m |
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 distance covered by a particle undergoing SHM in one time period is: (amplitude \(= A\))
1. zero
2. \(A\)
3. \(2 A\)
4. \(4 A\)
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. \(\pi ~\text{rad}\)
| 1. | \(e^{\omega t}\) | 2. | \(\text{log}_e(\omega t)\) |
| 3. | \(\text{sin}\omega t+ \text{cos}\omega t\) | 4. | \(e^{-\omega t}\) |
1. \(3n\)
2. \(4n\)
3. \(n\)
4. \(2n\)
A spring is stretched by \(5~\text{cm}\) by a force \(10~\text{N}\). The time period of the oscillations when a mass of \(2~\text{kg}\) is suspended by it is:
1. \(3.14~\text{s}\)
2. \(0.628~\text{s}\)
3. \(0.0628~\text{s}\)
4. \(6.28~\text{s}\)
| 1. | \(8\) | 2. | \(11\) |
| 3. | \(9\) | 4. | \(10\) |
During simple harmonic motion of a body, the energy at the extreme position is:
| 1. | both kinetic and potential |
| 2. | is always zero |
| 3. | purely kinetic |
| 4. | purely potential |
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