Q. No.Which of the following examples represent simple harmonic motion?
| 1. | The rotation of the earth about its axis. |
| 2. | The motion of an oscillating mercury column in a U-tube. |
| 3. | General vibrations of a polyatomic molecule about its equilibrium position. |
| 4. | A fan rotating with a constant angular velocity. |
1. \(\frac{\pi}{\omega}\)
2. \(\frac{4 \pi}{\omega}\)
3. \(\frac{3 \pi}{\omega}\)
4. \(\frac{2 \pi}{\omega}\)
:
| 1. | a simple harmonic function. |
| 2. | a simple harmonic function but not a periodic function. |
| 3. | both periodic and simple harmonic function. |
| 4. | only periodic function. |
A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. (Take the direction from A to B as the positive direction.) The signs of velocity, acceleration, and force on the particle when it is at 3 cm away from A going towards B are:
1. Zero, Negative, Negative
2. Negative, Zero, Zero
3. Negative, Negative, Negative
4. Positive, Positive, Positive
Which of the following relationships between the acceleration '\(a\)' and the displacement '\(x\)' of a particle involves simple harmonic motion?
| 1. | \(a = 0 . 7 x\) | 2. | \(a = - 200 x^{2} \) |
| 3. | \(a = - 10 x\) | 4. | \(a = 100 x^{3}\) |
A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?
1. 219 N
2. 196 N
3. 223 N
4. 225 N
The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed?
1. 50 m/min
2. 150 m/min
3. 100 m/min
4. 120 m/min
The acceleration due to gravity on the surface of the moon is 1.7 m . What is the time period of a simple pendulum on the surface of the moon if its time period on the surface of the earth is 3.5 s? (g on the surface of the earth is 9.8 m )
1. 7.3 s
2. 6.4 s
3. 5.5 s
4. 8.4 s
What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?
1. \(100\) s-1
2. zero
3. \(150\) s-1
4. none of these
A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?
1. \(\mathrm{T}=2 \pi \sqrt{\frac{1}{\sqrt{\mathrm{g}^2+\frac{\mathrm{v}^4}{\mathrm{R}^2}}}}\)
2. \(\mathrm{T}=4 \pi \sqrt{\frac{\mathrm{l}}{\mathrm{g}^2+\frac{\mathrm{v}^4}{\mathrm{R}^2}}}\)
3. \(\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{l}}{\mathrm{g}^2+\frac{\mathrm{v}^3}{\mathrm{R}^2}}}\)
4. \(\mathrm{T}=4 \pi \sqrt{\frac{1}{\sqrt{\mathrm{g}^2+\frac{\mathrm{v}^4}{\mathrm{R}^4}}}}\)
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