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

Subtopic:  Simple Harmonic Motion |
 65%
From NCERT
AIPMT - 1998
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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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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 |
 81%
From NCERT
AIPMT - 1998
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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 |
 66%
From NCERT
AIPMT - 1999
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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. lA=lB4

2. lA=4lB

3. lA=2lB & MA=2MB

4. lA=lB2 & MA=MB2

Subtopic:  Angular SHM |
 72%
From NCERT
AIPMT - 2000
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The total energy of the particle performing SHM depends on: 
1. \(k,\) \(a,\) \(m\)
2. \(k,\) \(a\)
3. \(k,\) \(a\)\(x \)
4. \(k,\) \(x \)

Subtopic:  Energy of SHM |
 68%
From NCERT
AIPMT - 2001
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When a mass is suspended separately by two different springs, in successive order, then the time period of oscillations is \(t _1\) and \(t_2\) respectively. If it is connected by both springs as shown in the figure below, then the time period of oscillation becomes \(t_0.\) The correct relation between \(t_0,\) \(t_1\) & \(t_2\) is:

           

1. t02=t12+t22

2. t0-2=t1-2+t2-2

3. t0-1=t1-1+t2-1

4. t0=t1+t2

Subtopic:  Combination of Springs |
 68%
From NCERT
AIPMT - 2002
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The displacement between the maximum potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is:

1. ±a2

2. +a

3. ±a

4. -1

Subtopic:  Energy of SHM |
 73%
From NCERT
AIPMT - 2002
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The time period of a mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be:
1. T/4
2. T
3. T/2
4. 2T

Subtopic:  Spring mass system |
 72%
From NCERT
AIPMT - 2003
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