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Q. No.Identify the correct definition:
| 1. | If after every certain interval of time, a particle repeats its motion, then the motion is called periodic motion. |
| 2. | To and fro motion of a particle is called oscillatory motion. |
| 3. | Oscillatory motion described in terms of single sine and cosine functions is called simple harmonic motion. |
| 4. | All of the above |
Subtopic: Types of Motion |
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The two-dimensional motion of a particle, described by \(\vec{r}=(\hat{i}+2\hat{j}) A~\text{cos}(\omega t) \) is a/an:
Choose the correct answer from the options given below:
| (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 |
Subtopic: Types of Motion |
53%
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A particle executes SHM with an amplitude \(A\) and the time period \(T\). If at \(t=0,\) the particle is at its origin (mean position), then the time instant when it covers a distance equal to \(2.5A\) will be:
| 1. | \( \frac{T}{12} \) | 2. | \(\frac{5 T}{12} \) |
| 3. | \( \frac{7 T}{12} \) | 4. | \(\frac{2 T}{3}\) |
Subtopic: Linear SHM |
57%
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The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
1. \(25~\text{Hz}\)
2. \(50~\text{Hz}\)
3. \(12.25~\text{Hz}\)
4. \(33.3~\text{Hz}\)
Subtopic: Simple Harmonic Motion |
74%
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A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resulting amplitude is equal to the amplitude of individual motions, the phase difference between them will be:
1. \(\frac{\pi}{3}\)
2. \(\frac{2\pi}{3}\)
3. \(\frac{\pi}{6}\)
4. \(\frac{\pi}{2}\)
1. \(\frac{\pi}{3}\)
2. \(\frac{2\pi}{3}\)
3. \(\frac{\pi}{6}\)
4. \(\frac{\pi}{2}\)
Subtopic: Linear SHM |
62%
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The motion of a particle varies with time according to the relation \(y= a\sin\omega t+ a\cos \omega t\). Then:
| 1. | the motion is oscillatory but not SHM. |
| 2. | the motion is SHM with an amplitude \(a\sqrt{2}\). |
| 3. | the motion is SHM with an amplitude \(\sqrt{2}\). |
| 4. | the motion is SHM with an amplitude \(a\). |
Subtopic: Simple Harmonic Motion |
73%
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Kinetic energy of a particle executing simple harmonic motion in straight line is \(pv^2\) and potential energy is \(qx^2,\) where \(v\) is speed at distance \(x\) from the mean position. The time period of the SHM is given by the expression:
1. \(2\pi \sqrt{\frac{q}{p}}\)
2. \(2\pi \sqrt{\frac{p}{q}}\)
3. \(2\pi \sqrt{\frac{q}{p+q}}\)
4. \(2\pi \sqrt{\frac{p}{p+q}}\)
1. \(2\pi \sqrt{\frac{q}{p}}\)
2. \(2\pi \sqrt{\frac{p}{q}}\)
3. \(2\pi \sqrt{\frac{q}{p+q}}\)
4. \(2\pi \sqrt{\frac{p}{p+q}}\)
Subtopic: Energy of SHM |
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The equation of motion of a particle is \({d^2y \over dt^2}+Ky=0 \) where \(K\) is a positive constant. The time period of the motion is given by:
| 1. | \(2 \pi \over K\) | 2. | \(2 \pi K\) |
| 3. | \(2 \pi \over \sqrt{K}\) | 4. | \(2 \pi \sqrt{K}\) |
Subtopic: Simple Harmonic Motion |
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The equation of an SHM is given as \(y = 3\sin\omega t+ 4\cos \omega t\) where \(y\) is in centimeters. The amplitude of the SHM will be?
| 1. | \(3~\text{cm}\) | 2. | \(3.5~\text{cm}\) |
| 3. | \(4~\text{cm}\) | 4. | \(5~\text{cm}\) |
Subtopic: Linear SHM |
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A particle executes linear SHM between \(x=A.\) The time taken to go from \(0\) to \(A/2\) is \(T_1\) and to go from \(A/2\) to \(A\) is \(T_2\) then:
| 1. | \(T_1<T_2\) | 2. | \(T_1>T_2\) |
| 3. | \(T_1=T_2\) |
4. | \(T_1= 2T_2\) |
Subtopic: Linear SHM |
74%
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