# The figure shows the circular motion of a particle. The radius of the circle, the period, the sense of revolution, and the initial position are indicated in the figure. The simple harmonic motion of the $$\mathrm{x\text-}$$projection of the radius vector of the rotating particle $$P$$ will be:                                       1. $$x \left( t \right) = B$$ $$\text{sin} \left(\dfrac{2 πt}{30}\right)$$ 2. $$x \left( t \right) = B$$ $$\text{cos} \left(\dfrac{πt}{15}\right)$$ 3. $$x \left( t \right) = B$$ $$\text{sin} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)$$ 4. $$x \left( t \right) = B$$ $$\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)$$

Subtopic:  Simple Harmonic Motion | Phasor Diagram |
51%
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Displacement versus time curve for a particle executing SHM is shown in the figure. Choose the correct statement/s.

 1 Phase of the oscillator is the same at t =0 s and t = 2 s. 2 Phase of the oscillator is the same at t =2 s and t=6 s. 3 Phase of the oscillator is the same at t = 1 s and t=7 s. 4 Phase of the oscillator is the same at t=1 s and t=5 s.

 1 1, 2 and 4 2 1 and 3 3 2 and 4 4 3 and 4
Subtopic:  Simple Harmonic Motion |
72%
From NCERT
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A particle of mass $$m$$ and charge $$\text-q$$ moves diametrically through a uniformly charged sphere of radius $$R$$ with total charge $$Q$$. The angular frequency of the particle's simple harmonic motion, if its amplitude $$<R$$, is given by:
1. $$\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR} }$$
2. $$\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR^2} }$$
3. $$\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR^3}}$$
4. $$\sqrt{\dfrac{m}{4 \pi \varepsilon_0 ~qQ} }$$

Subtopic:  Linear SHM |
57%
From NCERT
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From the given functions, identify the function which represents a periodic motion:

 1 $$e^{\omega t}$$ 2 $$\text{log}_e(\omega t)$$ 3 $$\text{sin}\omega t+ \text{cos}\omega t$$ 4 $$e^{-\omega t}$$

Subtopic:  Types of Motion |
88%
From NCERT
NEET - 2020
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The rotation of the earth about its axis is:

 1 periodic motion. 2 simple harmonic motion. 3 periodic and simple harmonic motion. 4 non-periodic motion.
Subtopic:  Types of Motion |
83%
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Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie in a straight line perpendicular to the paths of the two particles. The phase difference is:

 1 π / 6 2 0 3 2 π / 3 4 π
Subtopic:  Linear SHM |
56%
From NCERT
AIPMT - 2011
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A particle is executing SHM with time period T. If the time period of its total mechanical energy is T', then $\frac{{T}^{\text{'}}}{T}$ will be:

 1 2 2 $$1 \over 2$$ 3 Zero 4 Infinite
Subtopic:  Energy of SHM |
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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 |
92%
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If the time of mean position from amplitude (extreme) position is 6 seconds, then the frequency of SHM will be:

 1 $$0.01$$ Hz 2 $$0.02$$ Hz 3 $$0.03$$ Hz 4 $$0.04$$ Hz
Subtopic:  Simple Harmonic Motion |
68%
From NCERT
AIPMT - 1998
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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. $$4~\text{Hz}$$

Subtopic:  Linear SHM |
86%
From NCERT
AIPMT - 2005
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