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 |
 56%
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The velocity-time diagram of a harmonic oscillator is shown in the adjoining figure. The frequency of oscillation is

                                     

(1) 25 Hz           

(2) 50 Hz

(3) 12.25 Hz       

(4) 33.3 Hz

Subtopic:  Simple Harmonic Motion |
 73%
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The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is

                                                      

(1) 1 ×102 N/m               

(2) 150 N/m

(3) 0.667 × 102 N/m       

(4) 3 × 102 N/m

Subtopic:  Energy of SHM |
 63%
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A body performs S.H.M. . Its kinetic energy K varies with time t as indicated by graph

(a)    (b) 

(c)      (d) 

 

Subtopic:  Energy of SHM |
 75%
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The displacement of a body executing SHM is given by x= A sin (2πt + π/3). The first time from t = 0 when the velocity is maximum is :
1. 0.33 sec
2. 0.16 sec
3. 0.25 sec
4. 0.5 sec

Subtopic:  Phasor Diagram |
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The time period of a particle executing SHM is 8 sec. At t = 0 it is at the mean position. The ratio of the distance covered by the particle in the 1st second to the 2nd second is :

1. 12 + 1

2. 2

3. 12 

4. 2 + 1

Subtopic:  Phasor Diagram |
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Two particles are in SHM in a straight line. Amplitude A and time period T of both the particles are equal. At time t = 0, one particle is at displacement Y1 = + A and the other at Y2 = -A/2, and they are approaching towards each other. After what time they cross each other?
1. T/3
2. T/4
3. 5T/6
4. T/6

Subtopic:  Phasor Diagram |
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Two particles execute SHM of the same amplitude of \(20\) cm with the same time period along the same line about the same equilibrium position. The maximum distance between the two is \(20\) cm. Their phase difference in radians is:
1. \(\frac{2\pi}{3}\)
2. \(\frac{\pi}{2}\)
3. \(\frac{\pi}{3}\)
4. \(\frac{\pi}{4}\)

Subtopic:  Phasor Diagram |
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Two particles P and Q describe simple harmonic motions of the same period, the same amplitude, along the same line about the same equilibrium position O. When P and Q are on opposite sides of O at the same distance from O, they have the same speed of 1.2 m/s in the same direction. When their displacements are the same, they have the same speed of 1.6 m/s in opposite directions. The maximum velocity in m/s of either particle is 
1. 2.8
2. 2.5
3. 2.4
4. 2

Subtopic:  Phasor Diagram |
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The graph shows the variation of displacement of a particle executing SHM with time. We infer from this graph that:

   
 

1. the force is zero at the time \(T/8\).
2. the velocity is maximum at the time \(T/4\).
3. the acceleration is maximum at the time \(T\).
4. the P.E. is equal to the total energy at the time \(T/4\).

Subtopic:  Energy of SHM |
 65%
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