# 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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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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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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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. ${l}_{A}=4{l}_{B}$

3. ${l}_{A}=2{l}_{B}$ $&$ ${M}_{A}=2{M}_{B}$

4. ${l}_{A}=\frac{{l}_{B}}{2}$ $&$ ${M}_{A}=\frac{{M}_{B}}{2}$

Subtopic:  Angular SHM |
72%
From NCERT
AIPMT - 2000
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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
Subtopic:  Types of Motion |
79%
From NCERT
AIPMT - 2005
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The frequency of a spring is $$n$$ after suspending mass $$M.$$ Now, after mass $$4M$$ mass is suspended from the spring, the frequency will be:

 1 $$2n$$ 2 $$n/2$$ 3 $$n$$ 4 none of the above

Subtopic:  Spring mass system |
80%
From NCERT
AIPMT - 1998
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Which one of the following statements is true for the speed 'v' and the acceleration 'a' of a particle executing simple harmonic motion?

 1 The value of a is zero whatever may be the value of 'v'. 2 When 'v' is zero, a is zero. 3 When 'v' is maximum, a is zero. 4 When 'v' is maximum, a is maximum.
Subtopic:  Simple Harmonic Motion |
86%
From NCERT
AIPMT - 2004
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A spring elongates by a length 'L' when a mass 'M' is suspended to it. Now a tiny mass 'm' is attached to the mass 'M' and then released. The new time period of oscillation will be:

1.  $$2 \pi \sqrt{\frac{\left(\right. M + m \left.\right) l}{Mg}}$$

2. $$2 \pi \sqrt{\frac{ml}{Mg}}$$

3. $$2 \pi \sqrt{L / g}$$

4. $$2 \pi \sqrt{\frac{Ml}{\left(\right. m + M \left.\right) g}}$$

Subtopic:  Spring mass system |
59%
From NCERT
AIPMT - 1999
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The frequency of a simple pendulum in a free-falling lift will be:
1. zero
2. infinite
3. can't say
4. finite

Subtopic:  Angular SHM |
67%
From NCERT
AIPMT - 1999
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