Q. No.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 |
From the given functions, identify the function which represents a periodic motion:
| 1. | \(e^{\omega t}\) | 2. | \(\text{log}_e(\omega t)\) |
| 3. | \(\text{sin}\omega t+ \text{cos}\omega t\) | 4. | \(e^{-\omega t}\) |
The angular velocities of three bodies in simple harmonic motion are with their respective amplitudes as . If all the three bodies have the same mass and maximum velocity, then:
| 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. | \(A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2\) |
An SHM has an amplitude \(a\) and a time period \(T.\) The maximum velocity will be:
1. \({4a \over T}\)
2. \({2a \over T}\)
3. \({2 \pi \over T}\)
4. \({2a \pi \over T}\)
The equation of motion of a particle is \({d^2y \over dt^2}+Ky=0 \) where \(K\) is a positive constant. The time period of the motion is given by:
| 1. | \(2 \pi \over K\) | 2. | \(2 \pi K\) |
| 3. | \(2 \pi \over \sqrt{K}\) | 4. | \(2 \pi \sqrt{K}\) |
Displacement versus time curve for a particle executing SHM is shown in the figure. Choose the correct statement/s.
| 1. | Phase of the oscillator is the same at t =0 s and t = 2 s. |
| 2. | Phase of the oscillator is the same at t =2 s and t=6 s. |
| 3. | Phase of the oscillator is the same at t = 1 s and t=7 s. |
| 4. | Phase of the oscillator is the same at t=1 s and t=5 s. |
| 1. | 1, 2 and 4 | 2. | 1 and 3 |
| 3. | 2 and 4 | 4. | 3 and 4 |
The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
1. 25 Hz
2. 50 Hz
3. 12.25 Hz
4. 33.3 Hz
If the time of mean position from amplitude (extreme) position is 6 seconds, then the frequency of SHM will be:
| 1. | \(0.01\) Hz | 2. | \(0.02\) Hz |
| 3. | \(0.03\) Hz | 4. | \(0.04\) Hz |
The equation of an SHM is given as y=3sinωt + 4cosωt where y is in centimeters. The amplitude of the SHM will be?
| 1. | 3 cm | 2. | 3.5 cm |
| 3. | 4 cm | 4. | 5 cm |
Two simple harmonic motions of angular frequency 100 rad s -1 and 1000 rad have the same displacement amplitude. The ratio of their maximum acceleration will be:
1. 1:10
2. 1:102
3. 1:103
4. 1:104
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