Q. No.A particle executing SHM has a maximum speed of \(30\) cm/s and a maximum acceleration of \(60\) cm/s2. The period of oscillation is:
1. \(\pi \) s
2. \(\dfrac{\pi }{2}\) s
3. \(2\pi\) s
4. \(\dfrac{\pi }{4}\) s
1. \(\pi \) s
2. \(\dfrac{\pi }{2}\) s
3. \(2\pi\) s
4. \(\dfrac{\pi }{4}\) s
When a mass \(m\) is connected individually to two springs \(S_1\) and \(S_2,\) the oscillation frequencies are \(\nu_1\) and \(\nu_2.\) If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be:
| 1. | \(v_2+v_2\) | 2. | \(\sqrt{v_1^2+v_2^2}\) |
| 3. | \(\left(\dfrac{1}{v_1}+\dfrac{1}{v_1}\right)^{-1}\) | 4. | \(\sqrt{v_1^2-v_2^2}\) |
The following statements are given for a simple harmonic oscillator.
| (a) | Force acting is directly proportional to the displacement from the mean position and opposite to it. |
| (b) | Motion is periodic. |
| (c) | Acceleration of the oscillator is constant. |
| (d) | The velocity is periodic. |
Choose the correct alternatives:
1. (a), (b), (d)
2. (a), (c)
3. (b), (d)
4. (c), (d)
The (displacement-time) graph of a particle executing SHM is shown in the figure. Then:
| (a) | the force is zero at \(t=\dfrac{3T}{4}\) |
| (b) | the acceleration is maximum at \(t=\dfrac{4T}{4}\) |
| (c) | the velocity is maximum at \(t=\dfrac{T}{4}\) |
| (d) | the potential energy is equal to the kinetic energy of oscillation at \(t=\dfrac{T}{2}\) |
| 1. | (a), (b) and (d) only | 2. | (a), (b) and (c) only |
| 3. | (b), (c) and (d) only | 4. | (c) and (d) only |
A body is performing SHM, then its:
| (a) | average total energy per cycle is equal to its maximum kinetic energy. |
| (b) | average kinetic energy per cycle is equal to half of its maximum kinetic energy. |
| (c) | mean velocity for a complete cycle is equal to \(\dfrac{2}{\pi}\) times of its maximum velocity. |
| (d) | root mean square velocity is \(\dfrac{1}{\sqrt{2}}\) times of its maximum velocity. |
Choose the correct alternatives:
1. (a), (b), (d)
2. (a), (c)
3. (b), (d)
4. (b), (c), (d)
A mass \(M\) is attached to a spring system as shown in the figure. If the mass is displaced from its equilibrium position and then released, what is the time period of its oscillation?
1. \(2\pi \sqrt{\dfrac{M}{k}} \)
2. \(2\pi \sqrt{\dfrac{M}{2k}} \)
3. \(2\pi \sqrt{\dfrac{M}{4k}} \)
4. \(2\pi \sqrt{\dfrac{2M}{3k}} \)
The rotation of the earth about its axis is:
| (a) | periodic motion |
| (b) | simple harmonic motion |
| (c) | periodic but not simple harmonic motion |
| (d) | non-periodic motion |
Choose the correct alternatives:
1. (a), (b), (d)
2. (a), (c)
3. (b), (d)
4. (c), (d)
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)
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
The figure shows the circular motion of a particle. The radius of the circle, the period, the sense of revolution, and the initial position are indicated in the figure. The simple harmonic motion of the \({x\text-}\)projection of the radius vector of the rotating particle \(P\) will be:
1. \(x \left( t \right) = B\text{sin} \left(\dfrac{2 πt}{30}\right)\)
2. \(x \left( t \right) = B\text{cos} \left(\dfrac{πt}{15}\right)\)
3. \(x \left( t \right) = B\text{sin} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\) \(\)
4. \(x \left( t \right) = B\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)
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