- 1(current)
Q. No.Which, of the following, represents the displacement in simple harmonic motion?
| (A) | \(x=A\sin^2\omega t\) |
| (B) | \(x=A\sin\omega t+B\cos2\omega t\) |
| (C) | \(x=A\sin^2\omega t+B\cos2\omega t\) |
| 1. | A only | 2. | A and B |
| 3. | A and C | 4. | A, B and C |
Subtopic: Â Types of Motion |
Level 4: Below 35%
Hints
Two SHMs given by their displacements along the respective directions are superposed: \(x=A\sin\omega t~~~~(1^{\text{st}}~\text{SHM along }x\text{-axis})\\ y=A\sin\bigg(\omega t+{\large\frac{\pi}{2}}\bigg)~~~~(2^{\text{nd}}~\text{SHM along }y\text{-axis}).\)
The resultant motion is:
The resultant motion is:
| 1. | SHM along a straight line |
| 2. | SHM along a circular arc |
| 3. | uniform circular motion |
| 4. | motion along an elliptic path |
Subtopic: Â Types of Motion |
Level 3: 35%-60%
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Trains travel between station \(A\) and station \(B\): on the way up (from \(A~\text{to}~B \)) - they travel at a speed of \(80\text{ km/h},\) while on the return trip the trains travel at twice that speed. The services are maintained round the clock. Trains leave station \(A\) every \(30\text{ min}\) for station \(B\) and reach \(B\) in \(2\text{ hrs.}\) All trains operate continuously, without any rest at \(A\) or \(B.\)
| 1. | the frequency of trains leaving \(B\) must be twice as much as \(A\). |
| 2. | the frequency of trains leaving \(B\) must be half as much as \(A\). |
| 3. | the frequency of trains leaving \(B\) is equal to that at \(A\). |
| 4. | the situation is impossible to maintain unless larger number of trains are provided at \(A\). |
Subtopic: Â Types of Motion |
Level 3: 35%-60%
Hints
An elastic ball rebounds vertically to a height \(h\) above the ground, the period of its motion will be:
| 1. | \(\begin{aligned} \large\sqrt\frac{2h}{g} & \\ \end{aligned}\) | 2. | \(\begin{aligned} \large\sqrt\frac{8h}{g} & \\ \end{aligned}\) |
| 3. | \(\begin{aligned} \large\sqrt\frac{h}{2g} & \\ \end{aligned}\) | 4. | \(\begin{aligned} 2\large{\sqrt\frac{h}{g}} & \\ \end{aligned}\) |
Subtopic: Â Types of Motion |
Level 3: 35%-60%
Hints
- 1(current)
Q. No.
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