A block of mass m is attached to a massless spring having a spring constant k. The other end of the spring is fixed from the wall of a trolley, as shown in the figure. Spring is initially unstretched and the trolley starts moving toward the direction shown. Its velocity-time graph is also shown.

              

The energy of oscillation, as seen from the trolley is:

1.  32m26k

2.  9m28k

3.  9m232k

4.  8m29k

Subtopic:  Combination of Springs |
 66%
From NCERT
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A body of mass \(20\) g is executing SHM with amplitude \(5\) cm. When it passes through the equilibrium position its speed is \(20\) cm/s. What would be the distance from equilibrium when its speed becomes \(10\) cm/s?
1. \(\frac{5\sqrt{3}}{4}\) cm

2. \(\frac{5\sqrt{3}}{2}\) cm

3. \(\frac{25\sqrt{7}}{2}\) cm

4. \(5\sqrt{3}\) cm

Subtopic:  Simple Harmonic Motion |
 76%
From NCERT
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For a simple harmonic oscillator, a velocity-time diagram is shown. The angular frequency of oscillation is:

                

1.  242 rad/s

2.  25π4 rad/s

3.  25 rad/s

4.  25π rad/s

Subtopic:  Simple Harmonic Motion |
 64%
From NCERT
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In an S.H.M, when the displacement is one-fourth of the amplitude, the ratio of total energy to the potential energy is 

1.  16: 1

2.  1: 16

3.  1: 8

4.  8: 1

Subtopic:  Energy of SHM |
 79%
From NCERT
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A particle executing S.H.M. Its displacement x varies with time t as x=8sin4t+6cos4t.  The maximum  velocity of the particle will be:

1.  20 unit

2.  10 unit

3.  40 unit

4.  5 unit

Subtopic:  Simple Harmonic Motion |
 79%
From NCERT
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The amplitude of oscillation for a particle executing S.H.M with angular frequency πrad/s and maximum acceleration 5π2 m/s2 is

1.  25 cm

2.  25 m

3.  5 cm

4.  5 m

Subtopic:  Angular SHM |
 72%
From NCERT
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Which of the following statements is true for an ideal simple pendulum?

1. The expression for the time period is true only for the oscillation of infinitely small amplitude.
2. The motion of the bob is rotatory.
3. The buoyancy of air has an appreciable effect on the motion of the bob.
4. All of these.
Subtopic:  Simple Harmonic Motion |
From NCERT
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A mass of 30 gm is attached with two springs having spring constants 100 N/m and 200 N/m and other ends of springs are attached to rigid walls as shown in the given figure. The angular frequency of oscillation is: (Ground is smooth)

                      

1.  1002π rad/s 

2.  100π rad/s

3.  100 rad/s

4.  200π rad/s

Subtopic:  Combination of Springs |
 60%
From NCERT
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If a bob of the simple pendulum having negative charge q is made to oscillate in a uniform electric field acting vertically upward direction, then its time period:

1.  Increases

2.  Decreases

3.  No effect of the electric field

4.  Decreases or increases

Subtopic:  Simple Harmonic Motion |
 61%
From NCERT
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A simple pendulum of length l and bob of mass m is executing S.H.M with amplitude A. The maximum tension in the string will be

1.  mgll + A

2.  mgl2 + A2l2

3.  mgl2l2 + A2

4.  mgl + Al

Subtopic:  Angular SHM |
 57%
From NCERT
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