Q. No.The motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is
| (a) | simple harmonic motion |
| (b) | non-periodic motion |
| (c) | periodic motion |
| (d) | periodic but not SHM |
Choose the correct alternatives:
1. (a), (c)
2. (a), (d)
3. (c), (d)
4. (b), (c)
| 1. | a straight line and is periodic. |
| 2. | a circle and is non-periodic. |
| 3. | an ellipse and is periodic. |
| 4. | a parabola and is non-periodic. |
The equation of motion of a particle is \(x =a \text{cos} ( \alpha t )^{2}\). The motion is:
1. periodic but not oscillatory
2. periodic and oscillatory
3. oscillatory but not periodic
4. neither periodic nor oscillatory
| (a) | \(\sin\omega t+ \cos\omega t\) |
| (b) | \(\sin\omega t+ \cos2\omega t+ \sin4\omega t\) |
2. \(\dfrac{2 \pi}{\omega} \text{ for both}\)
3. \(\dfrac{2 \pi}{3 \omega} \text{ for both}\)
4. \(\dfrac{3 \pi}{\omega} \text{ and } \dfrac{2 \pi}{\omega}\)
The distance moved by a particle in simple harmonic motion in one time period is.
1. \(A\)
2. \(2A\)
3. \(4A\)
4. zero
| Assertion (A): | The combination of \(y=\text{sin}\omega t+\text{cos}2\omega t\) is not a simple harmonic function even though it is periodic. |
| Reason (R): | All periodic functions satisfy the relation \( \dfrac{d^{2} y}{d t^{2}}=-k y \). |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)
are superposed on a particle, along \(x\) and \(y\) directions. The resultant of these motions is:
| 1. | circular motion |
| 2. | SHM along \(x\)-axis |
| 3. | SHM along \(y\)-axis |
| 4. | SHM, but along a direction other than \(x\) or \(y\)-axis |
The displacement of a particle is represented by the equation \(y= 3 \cos \left(\frac{\pi}{4}-\omega t \right)\). The motion of the particle is:
| 1. | simple harmonic with period \(\dfrac{2\pi}{\omega}\) |
| 2. | simple harmonic with period \(\dfrac{\pi}{\omega}\) |
| 3. | periodic but not simple harmonic |
| 4. | non-periodic |
The displacement of a particle is represented by the equation \(y =\sin^{3}~\omega t\). The motion is:
1. non-periodic.
2. periodic but not simple harmonic.
3. simple harmonic with period \(2\pi / \omega\).
4. simple harmonic with period \(\pi / \omega\).
The displacement of a particle varies with time according to the relation, \(y=a~\text{sin} \omega t+b~\text{cos} \omega t.\)
| 1. | the motion is oscillatory but not SHM |
| 2. | the motion is SHM with amplitude \(a+b\) |
| 3. | the motion is SHM with amplitude \(a^{2}+b^{2}\) |
| 4. | the motion is SHM with amplitude \(\sqrt{a^{2}+b^{2}}\) |
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