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 |
 93%
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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 angular velocities of three bodies in simple harmonic motion are \(\omega_1, \omega_2, \omega_3\) with their respective amplitudes as \(A_1, A_2, A_3.\) If all the three bodies have the same mass and maximum velocity, then:
1. \(A_1 \omega_1=A_2 \omega_2=A_3 \omega_3\)
2. \(A_1 \omega_1^2=A_2 \omega_2^2=A_3 \omega_3^2\)
3. \(A_1^2 \omega_1=A_2^2 \omega_2=A_3^2 \omega_3\)
4. \(A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2\)
Subtopic:  Simple Harmonic Motion |
 91%
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An SHM has an amplitude \(a\) and a time period \(T.\) The maximum velocity will be:
1. \({4a \over T}\)       
2. \({2a \over T}\)
3. \({2 \pi \over T}\)
4. \({2a \pi \over T}\)
Subtopic:  Simple Harmonic Motion |
 90%
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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 |
 76%
From NCERT
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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 \(t = 0~\text{s}~\text{and}~t = 2~\text{s}\).
2. Phase of the oscillator is the same at \(t = 2~\text{s}~\text{and}~t = 6~\text{s}\).
3. Phase of the oscillator is the same at \(t = 1~\text{s}~\text{and}~t = 7~\text{s}\).
4. Phase of the oscillator is the same at \(t = 1~\text{s}~\text{and}~t = 5~\text{s}\).
1. \(1,2~\text{and}~4\) 2. \(1~\text{and}~3\)
3. \(2~\text{and}~4\) 4. \(3~\text{and}~4\)
Subtopic:  Simple Harmonic Motion |
 72%
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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 |
 73%
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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. \(0.01~\text{Hz}\) 2. \(0.02~\text{Hz}\)
3. \(0.03~\text{Hz}\) 4. \(0.04~\text{Hz}\)
Subtopic:  Simple Harmonic Motion |
 68%
From NCERT
AIPMT - 1998
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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 |
 90%
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Two simple harmonic motions of angular frequency \(100~\text{rad s}^{-1}\) and \(1000~\text{rad s}^{-1}\) have the same displacement amplitude. The ratio of their maximum acceleration will be:
1. \(1:10\)
2. \(1:10^{2}\)
3. \(1:10^{3}\)
4. \(1:10^{4}\)

Subtopic:  Linear SHM |
 86%
From NCERT
NEET - 2008
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