Q. No.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. \(\dfrac{3\pi}{2}\text{rad}\)
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. | \(e^{-\omega t}\) |
The distance covered by a particle undergoing SHM in one time period is: (amplitude \(= A\))
1. zero
2. \(A\)
3. \(2 A\)
4. \(4 A\)
1. \(\frac{\pi}{6}\)
2. \(0\)
3. \(\frac{2\pi}{3}\)
4. \(\pi\)
Two pendulums suspended from the same point have lengths of \(2\) m and \(0.5\) m. If they are displaced slightly and released, then they will be in the same phase when the small pendulum has completed:
1. \(2\) oscillations
2. \(4\) oscillations
3. \(3\) oscillations
4. \(5\) oscillations
| 1. | \(0.01~\text{Hz}\) | 2. | \(0.02~\text{Hz}\) |
| 3. | \(0.03~\text{Hz}\) | 4. | \(0.04~\text{Hz}\) |
A particle executing simple harmonic motion of amplitude \(5~\text{cm}\) has a maximum speed of \(31.4~\text{cm/s}.\) The frequency of its oscillation will be:
1. \(1~\text{Hz}\)
2. \(3~\text{Hz}\)
3. \(2~\text{Hz}\)
4. \(4~\text{Hz}\)
Two spherical bobs of masses \(M_A\) and \(M_B\) are hung vertically from two strings of length \(l_A\) and \(l_B\) respectively. If they are executing SHM with frequency as per the relation \(f_A=2f_B,\) Then:
1. \(l_A = \frac{l_B}{4}\)
2. \(l_A= 4l_B\)
3. \(l_A= 2l_B~\&~M_A=2M_B\)
4. \(l_A= \frac{l_B}{2}~\&~M_A=\frac{M_B}{2}\)
The circular motion of a particle with constant speed is:
| 1. | Periodic and simple harmonic | 2. | Simple harmonic but not periodic |
| 3. | Neither periodic nor simple harmonic | 4. | Periodic but not simple harmonic |
| 1. | \(2n\) | 2. | \(n/2\) |
| 3. | \(n\) | 4. | none of the above |
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