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A particle executes SHM with an amplitude \(A\) and the time period \(T\). If at \(t=0,\) the particle is at its origin (mean position), then the time instant when it covers a distance equal to \(2.5A\) will be:
| 1. | \( \frac{T}{12} \) | 2. | \(\frac{5 T}{12} \) |
| 3. | \( \frac{7 T}{12} \) | 4. | \(\frac{2 T}{3}\) |
Subtopic: Â Linear SHM |
 58%
Level 3: 35%-60%
Hints
The displacement of a particle varies according to the relation:
\(x=4\left({\cos{\pi t}+\sin{\pi t}}\right) \)
The amplitude of the particle is:
\(x=4\left({\cos{\pi t}+\sin{\pi t}}\right) \)
The amplitude of the particle is:
| 1. | \(8\) | 2. | \(-4 \) |
| 3. | \(4\) | 4. | \(4\sqrt{2} \) |
Subtopic: Â Linear SHM |
 66%
Level 2: 60%+
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A particle moves so that its acceleration \(a\) is given by; \(a=-bx, \) where \(x \) is the displacement from the equilibrium position and \(b\) is a constant. The period of oscillation is:
| 1. | \({2}{\pi}\sqrt{b} \) | 2. | \(\dfrac{2\pi }{\sqrt{b}}\) |
| 3. | \(\dfrac{2\pi }{b}\) | 4. | \(2\sqrt{\dfrac{\pi }{b}} \) |
Subtopic: Â Linear SHM |
 86%
Level 1: 80%+
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A body oscillates with SHM according to the equation (in SI units), \(x= 5\cos\left[2\pi t +\dfrac{\pi}{4}\right].\) At \(t = 1.5 \text{ s},\) acceleration of the body will be:
1. \(140 \text{ cm} / \text{s}^2 \)
2. \(160 \text{ m} / \text{s}^2 \)
3. \(140 \text{ m} / \text{s}^2 \)
4. \(14 \text{ m} / \text{s}^2\)
1. \(140 \text{ cm} / \text{s}^2 \)
2. \(160 \text{ m} / \text{s}^2 \)
3. \(140 \text{ m} / \text{s}^2 \)
4. \(14 \text{ m} / \text{s}^2\)
Subtopic: Â Linear SHM |
 61%
Level 2: 60%+
Hints
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A particle moves in the x-y plane according to the equation
\(x = A \cos^2 \omega t\) and \(y = A \sin^2 \omega t\)
Then, the particle undergoes:
| 1. | uniform motion along the line \(x + y = A\) |
| 2. | uniform circular motion along \(x^2 + y^2 = A^2\) |
| 3. | SHM along the line \(x + y = A\) |
| 4. | SHM along the circle \(x^2 + y^2 = A^2\) |
Subtopic: Â Linear SHM |
Level 3: 35%-60%
Hints
A particle executes simple harmonic motion between \(x=-A\) and \(x=+A.\) The time taken for it to move from \(0\) to \(A/2\) is \(T_1\) and the time to move from \(A/2\) to \(A\) is \(T_2.\) Then:
1. \(T_{1}<T_{2}\)
2. \(T_{1}>T_{2}\)
3. \(T_{1}=T_{2}\)
4. \(T_{1}=2 T_{2}\)
1. \(T_{1}<T_{2}\)
2. \(T_{1}>T_{2}\)
3. \(T_{1}=T_{2}\)
4. \(T_{1}=2 T_{2}\)
Subtopic: Â Linear SHM |
 74%
Level 2: 60%+
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