Q. No.A particle is executing SHM along a straight line. Its velocities at distances \(x_1\) and \(x_2\) from the mean position are \(v_1\) and \(v_2\), respectively. Its time period is:
1.
\(2 \pi \sqrt{\dfrac{x_{1}^{2}+x_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}}~\)
2.
\(2 \pi \sqrt{\dfrac{{x}_{2}^{2}-{x}_{1}^{2}}{{v}_{1}^{2}-{v}_{2}^{2}}}\)
3.
\(2 \pi \sqrt{\dfrac{v_{1}^{2}+v_{2}^{2}}{x_{1}^{2}+x_{2}^{2}}}\)
4.
\(2 \pi \sqrt{\dfrac{v_{1}^{2}-v_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}}\)
The oscillation of a body on a smooth horizontal surface is represented by the equation, \(X=A \text{cos}(\omega t)\),
where \(X=\) displacement at time \(t,\) \(\omega=\) frequency of oscillation.
Which one of the following graphs correctly shows the variation of acceleration, \(a\) with time, \(t?\)
(\(T=\) time period) \(a~~O~~T~~t~~\)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
The damping force of an oscillator is directly proportional to the velocity. The units of the constant of proportionality are:
1. kg-msec-1
2. kg-msec-2
3. kg-sec-1
4. kg-sec
1. Only (IV) does not represent SHM
2. (I) and (III)
3. (I) and (II)
4. Only (I)
A particle of mass \(m\) is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
The displacement of a particle along the x-axis is given by, x = asin2t. The motion of the particle corresponds to:
| 1. | simple harmonic motion of frequency |
| 2. | simple harmonic motion of frequency |
| 3. | non-simple harmonic motion |
| 4. | simple harmonic motion of frequency |
1. \(T\)
2. \(\frac{T}{\sqrt{2}}\)
3. \(2T\)
4. \(\sqrt{2}T\)
1. \(\frac{\pi a\sqrt3}{2T}\)
2. \(\frac{\pi a}{T}\)
3. \(\frac{3\pi^2 a}{T}\)
4. \(\frac{\pi a\sqrt3}{T}\)
1. Acceleration = -k0x + k1x2
2. Acceleration = -k(x+a)
3. Acceleration = k(x+a)
4. Acceleration = kx
1. 1: 10
2. 1: 102
3. 1: 103
4. 1: 104
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