Q. No.A particle executes linear simple harmonic motion with amplitude of \(3~\text{cm}\). When the particle is at \(2~\text{cm}\) from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:
1. \(\dfrac{\sqrt5}{2\pi}\)
2. \(\dfrac{4\pi}{\sqrt5}\)
3. \(\dfrac{4\pi}{\sqrt3}\)
4. \(\dfrac{\sqrt5}{\pi}\)
1. \(\dfrac{\sqrt5}{2\pi}\)
2. \(\dfrac{4\pi}{\sqrt5}\)
3. \(\dfrac{4\pi}{\sqrt3}\)
4. \(\dfrac{\sqrt5}{\pi}\)
A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is \(20\text{ m/s}^2\) at a distance of \(5\text{ m}\) from the mean position. The time period of oscillation is:
1. \(2\pi \text{ s}\)
2. \(\pi \text{ s}\)
3. \(2 \text{ s}\)
4. \(1 \text{ s}\)
A particle is executing a simple harmonic motion. Its maximum acceleration is \(\alpha\) and maximum velocity is \(\beta.\) Then its time period of vibration will be:
1. \(\dfrac {\beta^2}{\alpha^2}\)
2. \(\dfrac {\beta}{\alpha}\)
3. \(\dfrac {\beta^2}{\alpha}\)
4. \(\dfrac {2\pi \beta}{\alpha}\)
When two displacements are represented by \(y_1 = a \text{sin}(\omega t)\) and \(y_2 = b\text{cos}(\omega t)\) are superimposed, then the motion is:
| 1. | not simple harmonic. |
| 2. | simple harmonic with amplitude \(\dfrac{a}{b}\). |
| 3. | simple harmonic with amplitude \(\sqrt{a^2+b^{2}}.\) |
| 4. | simple harmonic with amplitude \(\dfrac{a+b}{2}\). |
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)
| 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 |
© 2025 GoodEd Technologies Pvt. Ltd.