For a particle executing SHM the displacement \(x \) is given by, \(A\cos \omega t.\)  Identify the graph which represents the variation of potential energy (P.E.) as a function of time \(t\) and displacement \(x.\)

   
1. I, III
2. II, IV
3. II, III
4. I, IV

Subtopic:  Energy of SHM |
 57%
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A body is performing SHM, then its:

(a) average total energy per cycle is equal to its maximum kinetic energy.
(b) average kinetic energy per cycle is equal to half of its maximum kinetic energy.
(c) mean velocity for a complete cycle is equal to \(\dfrac{2}{\pi}\) times of its maximum velocity.
(d) root mean square velocity is \(\dfrac{1}{\sqrt{2}}\) times of its maximum velocity.

Choose the correct alternatives:
1. (a), (b), (d)

2. (a), (c)

3. (b), (d)

4. (b), (c), (d)

Subtopic:  Energy of SHM |
 54%
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A particle of mass \(m\) executes SHM along a straight line with an amplitude \(A\) and frequency \(f.\)

Assertion (A): The kinetic energy of the particle undergoes oscillation with a frequency \(2f.\)
Reason (R): Velocity of the particle, \(v = {\dfrac{dx}{dt}}\), its kinetic energy equals \({\dfrac 12}mv^2\) and the particle oscillates sinusoidally with a frequency \(f\).
 
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. (A) is False but (R) is True.
Subtopic:  Energy of SHM |
 52%
From NCERT
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Given below are two statements: 
Assertion (A):  The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola. 
Reason (R):  Potential energy and kinetic energy do not vary linearly with position.
 
1.  Both (A) and (R) are true and (R) is the correct explanation of (A).
2. Both (A) and (R) are true but (R) is not the correct explanation of (A).
3. (A) is true but (R) is false.
4. Both (A) and (R) are false.
Subtopic:  Energy of SHM |
From NCERT
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Given below are two statements: 
Statement I: If the acceleration of a particle is directed towards a fixed point, and proportional to the distance from that point – the motion is SHM.
Statement II: During SHM, the kinetic energy of the particle oscillates at twice the frequency of the SHM.
 
1. Statement I is incorrect and Statement II is correct.
2. Both Statement I and Statement II are correct.
3. Both Statement I and Statement II are incorrect.
4. Statement I is correct and Statement II is incorrect.
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 |
 85%
From NCERT
NEET - 2022
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