All the surfaces are smooth and the system, given below, is oscillating with an amplitude \(\mathrm{A}.\) What is the extension of spring having spring constant \(\mathrm{k_1},\) when the block is at the extreme position?
1. | \({k_1 \over k_1+k_2} \text{A}\) | 2. | \({k_2A \over k_1+k_2}\) |
3. | \(\mathrm{A}\) | 4. | \(\text{A} \over 2\) |
The displacement-time graph of a particle executing SHM is shown in the figure. Its displacement equation will be: (Time period = 2 second)
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A spring is having a spring constant k. It is cut into two parts A and B whose lengths are in the ratio of m:1. The spring constant of part A will be
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3. k
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In a simple harmonic oscillation, the graph of acceleration against displacement for one complete oscillation will be:
1. an ellipse
2. a circle
3. a parabola
4. a straight line
A particle executing SHM crosses points A and B with the same velocity. Having taken 3 s in passing from A to
B, it returns to B after another 3 s. The time period of the SHM will be:
1. | 15 s | 2. | 6 s |
3. | 12 s | 4. | 9 s |
The amplitude of a simple harmonic oscillator is \(A\) and speed at the mean position is \(v_0\) .The speed of the oscillator at the position \(x={A \over \sqrt{3}}\) will be:
1. | \(2v_0 \over \sqrt{3}\) | 2. | \(\sqrt{2}v_0 \over 3\) |
3. | \({2 \over 3}v_0\) | 4. | \(\sqrt{2}v_0 \over \sqrt{3}\) |
Which of the following examples represent simple harmonic motion?
1. | The rotation of the earth about its axis. |
2. | The motion of an oscillating mercury column in a U-tube. |
3. | General vibrations of a polyatomic molecule about its equilibrium position. |
4. | A fan rotating with a constant angular velocity. |
Which of the following relationships between the acceleration '\(a\)' and the displacement '\(x\)' of a particle involves simple harmonic motion?
1. | \(a = 0 . 7 x\) | 2. | \(a = - 200 x^{2} \) |
3. | \(a = - 10 x\) | 4. | \(a = 100 x^{3}\) |
A spring having a spring constant of 1200 N/m is mounted on a horizontal table as shown in the figure. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. The frequency of oscillations will be:
1. | \(3.0~\text{s}^{-1}\) | 2. | \(2.7~\text{s}^{-1}\) |
3. | \(1.2~\text{s}^{-1}\) | 4. | \(3.2~\text{s}^{-1}\) |
Acceleration of the particle at s from the given displacement (y) versus time (t) graph will be?
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4. Zero