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. | \(\text{A} \over 2\) |
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
1.
2.
3. k
4.
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. | \(9~\text{s}\) |
1. | \(2v_0 \over \sqrt{3}\) | 2. | \(\sqrt{2}v_0 \over 3\) |
3. | \({2 \over 3}v_0\) | 4. | \(\sqrt{\frac{2}{3}}v_0\) |
1. | The rotation of the earth about its axis. |
2. | The motion of an oscillating mercury column in a \(U\text-\)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. | \(3.2~\text{s}^{-1}\) |