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 damped oscillation, mass is 2 kg and spring constant is 500 N/m and damping coefficient is 1 kg s–1. If the mass is displaced by 20 cm from its mean position and released, then what will be the value of its mechanical energy after 4 seconds?
1. 2.37 J
2. 1.37 J
3. 10 J
4. 5 J
1. \(x= 10\sin\left(\pi t+\frac{\pi}{6}\right)\)
2. \(x= 10\sin\left(\pi t\right)\)
3. \(x= 10\cos\left(\pi t\right)\)
4. \(x= 5\sin\left(\pi t+\frac{\pi}{6}\right)\)
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. | \(\text{A} \over 2\) |
1. | \(2v_0 \over \sqrt{3}\) | 2. | \(\sqrt{2}v_0 \over 3\) |
3. | \({2 \over 3}v_0\) | 4. | \(\sqrt{\frac{2}{3}}v_0\) |
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
1. | \(15~\text{s}\) | 2. | \(6~\text{s}\) |
3. | \(12~\text{s}\) | 4. | \(9~\text{s}\) |
Acceleration of the particle at \(t = \frac{8}{3}~\text{s}\) from the given displacement \((y)\) versus time \((t)\) graph will be?
1. \(\frac{\sqrt{3}\pi^2}{4}~\text{cm/s}^2\)
2. \(-\frac{\sqrt{3}\pi^2}{4}~\text{cm/s}^2\)
3. \(-\pi^2~\text{cm/s}^2\)
4. zero
1. | the gravity of the earth | 2. | the mass of the block |
3. | spring constant | 4. | both (2) & (3) |
A body executes oscillations under the effect of a small damping force. If the amplitude of the body reduces by 50% in 6 minutes, then amplitude after the next 12 minutes will be [initial amplitude is ] -
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