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 \(t=\dfrac{T}{2}\) |
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 particle is in linear simple harmonic motion between two points \(A\) and \(B,\) \(10~\text{cm}\) apart (figure.) Take the direction from \(A\) to \(B\) as the positive direction.
(a) | The sign of velocity, acceleration and force on the particle, when it is \(3~\text{cm}\) away from \(A\) going towards \(B,\) are positive. |
(b) | The sign of velocity of the particle at \(C\) going towards \(B\) is negative. |
(c) | The sign of velocity, acceleration and force on the particle, when it is \(4~\text{cm}\) away from \(B\) going towards \(A,\) are negative. |
(d) | The sign of acceleration and force on the particle when it is at point \(B\) is negative. |
The correct statement/s is/are:
1. (a), (b), (d)
2. (a), (c), (d)
3. (b), (c), (d)
4. (c), (d)
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)
When a mass \(m\) is connected individually to two springs \(S_1\) and \(S_2,\) the oscillation frequencies are \(v_1\) and \(v_2.\) 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. | \(\sqrt{v_1^2-v_2^2}\) |
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
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 \(\mathrm{x\text-}\)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. \(x \left( t \right) = B\) \(\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)