A particle of mass \(m\) is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?
           

1. 2.
3. 4.
Subtopic:  Energy of SHM |
Level 3: 35%-60%
AIPMT - 2011
Hints

A particle executing simple harmonic motion has a kinetic energy of \(K_0 \cos^2(\omega t)\). The values of the maximum potential energy and the total energy are, respectively:
1. \(0~\text{and}~2K_0\)
2. \(\frac{K_0}{2}~\text{and}~K_0\)
3. \(K_0~\text{and}~2K_0\)
4. \(K_0~\text{and}~K_0\)
Subtopic:  Energy of SHM |
 64%
Level 2: 60%+
AIPMT - 2007
Hints

A particle of mass \(m\) oscillates with simple harmonic motion between points \(x_1\) and \(x_2\), the equilibrium position being \(O\). Its potential energy is plotted. It will be as given below in the graph:

1. 2.
3. 4.
Subtopic:  Energy of SHM |
 86%
Level 1: 80%+
AIPMT - 2003
Hints

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The potential energy of a simple harmonic oscillator, when the particle is halfway to its endpoint, will be:
1. \(\frac{2E}{3}\)
2. \(\frac{E}{8}\)
3. \(\frac{E}{4}\)
4. \(\frac{E}{2}\)

Subtopic:  Energy of SHM |
 82%
Level 1: 80%+
AIPMT - 2003
Hints

The displacement between the maximum potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is:
1. \(\pm \frac{a}{2}\)
2. \(+a\)
3. \(\pm a\)
4. \(-1\)

Subtopic:  Energy of SHM |
 76%
Level 2: 60%+
AIPMT - 2002
Hints

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 |
 72%
Level 2: 60%+
AIPMT - 2001
Hints

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