Identify the correct definition:
1. | If after every certain interval of time, a particle repeats its motion, then the motion is called periodic motion. |
2. | To and fro motion of a particle is called oscillatory motion. |
3. | Oscillatory motion described in terms of single sine and cosine functions is called simple harmonic motion. |
4. | All of the above |
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1. | \(e^{\omega t}\) | 2. | \(\text{log}_e(\omega t)\) |
3. | \(\text{sin}\omega t+ \text{cos}\omega t\) | 4. | \(e^{-\omega t}\) |
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The rotation of the earth about its axis is:
1. | periodic motion |
2. | simple harmonic motion |
3. | periodic and simple harmonic motion |
4. | non-periodic motion |
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The circular motion of a particle with constant speed is:
1. | Periodic and simple harmonic | 2. | Simple harmonic but not periodic |
3. | Neither periodic nor simple harmonic | 4. | Periodic but not simple harmonic |
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Which one of the following is not an example of simple harmonic motion?
1. | the motion of the Moon around the Earth as observed from Mars. |
2. | the ripples produced when a stone is dropped into a tank of water. |
3. | a weight moving up and down at the end of a spring. |
4. | the motion of a ball on the floor. |
List-I | List-II |
(a) motion with constant speed | (i) SHM |
(b) motion with constant acceleration | (ii) uniform circular motion |
(c) oscillatory motion | (iii) projectile motion |
(d) random motion | (iv) molecular motion in gas |
1. | a - (iv), b - (ii), c - (iii), d - (i) |
2. | a - (i), b - (iii), c - (ii), d - (iv) |
3. | a - (ii), b - (iii), c - (i), d - (iv) |
4. | a - (ii), b - (iii), c - (iv), d - (i) |
1. | \(A_1 \omega_1=A_2 \omega_2=A_3 \omega_3\) |
2. | \(A_1 \omega_1^2=A_2 \omega_2^2=A_3 \omega_3^2\) |
3. | \(A_1^2 \omega_1=A_2^2 \omega_2=A_3^2 \omega_3\) |
4. | \(A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2\) |
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If a particle in SHM has a time period of \(0.1\) s and an amplitude of \(6\) cm, then its maximum velocity will be:
1. \(120 \pi\) cm/s
2. \(0.6 \pi\) cm/s
3. \(\pi\) cm/s
4. \(6\) cm/s
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