Q. No.The figure depicts four \(({x\text-t})\) plots for the linear motion of a particle.
(a)
(b)
(c)
(d)
Which of the following is true?
1.
(a) is periodic but (c) is not periodic
2.
(b) is periodic but (d) is not periodic.
3.
(b) and (d) are periodic.
4.
only (c) is periodic.
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 functions. |
| 4. | only periodic function. |
A particle is in linear simple harmonic motion between two points, \(A\) and \(B\), \(10~\text{cm}\) 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 \(3~\text{cm}\) 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
A spring having a spring constant of \(1200\) N/m is mounted on a horizontal table as shown in the figure. A mass of \(3\) kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of \(2.0\) cm and released. The frequency of oscillations will be:
| 1. | \(3.0~\text{s}^{-1}\) | 2. | \(2.7~\text{s}^{-1}\) |
| 3. | \(1.2~\text{s}^{-1}\) | 4. | \(3.2~\text{s}^{-1}\) |
A spring having a spring constant of \(1200\) N/m is mounted on a horizontal table as shown in the figure. A mass of \(3\) kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of \(2.0\) cm and released. The maximum acceleration of the mass is:
| 1. | \(6\) ms–2 | 2. | \(8\) ms–2 |
| 3. | \(3.3\) ms–2 | 4. | \(5.1\) ms–2 |
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
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