A particle executing simple harmonic motion with amplitude \(A\) has the same potential and kinetic energies at the displacement:
1. \(2\sqrt{A}\) 2. \(\dfrac{A}{2}\)
3. \(\dfrac{\mathrm{A}}{\sqrt{2}}\) 4. \(A\sqrt{2}\)
Subtopic:  Energy of SHM |
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During simple harmonic motion of a body, the energy at the extreme position is:

1.  both kinetic and potential
2. is always zero
3. purely kinetic
4. purely potential
Subtopic:  Energy of SHM |
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Match List-I with List-II.
List-I
(\(x \text{-}y\) graphs)
List-II
(Situations)
(a) (i) Total mechanical energy is conserved
(b)   (ii) Bob of a pendulum is oscillating under negligible air friction
(c)   (iii) Restoring force of a spring
(d)   (iv) Bob of a pendulum is oscillating along with air friction

Choose the correct answer from the options given below:
(a) (b) (c) (d)
1. (iv) (ii) (iii) (i)
2. (iv) (iii) (ii) (i)
3. (i) (iv) (iii) (ii)
4. (iii) (ii) (i) (iv)
Subtopic:  Energy of SHM |
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If a body is executing simple harmonic motion with frequency \(n\), then the frequency of its potential energy is:
1. \(3n\) 2. \(4n\)
3. \(n\) 4. \(2n\)
Subtopic:  Energy of SHM |
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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 |
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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 |
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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 |
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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 |
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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. \(\pm \frac{a}{2}\)
2. \(+a\)
3. \(\pm a\)
4. \(-1\)

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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 |
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