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

Subtopic:  Types of Motion |
92%
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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 $$e^{-\omega t}$$

Subtopic:  Types of Motion |
88%
From NCERT
NEET - 2020
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The angular velocities of three bodies in simple harmonic motion are ${\omega }_{1},$ ${\omega }_{2},$ ${\omega }_{3}$ with their respective amplitudes as ${A}_{1},$ ${A}_{2},$ ${A}_{3}$. 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 $$A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2$$
Subtopic:  Simple Harmonic Motion |
90%
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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. $${2a \pi \over T}$$

Subtopic:  Simple Harmonic Motion |
90%
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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 $$2 \pi \sqrt{K}$$
Subtopic:  Simple Harmonic Motion |
75%
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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
Subtopic:  Simple Harmonic Motion |
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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

Subtopic:  Simple Harmonic Motion |
73%
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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
Subtopic:  Simple Harmonic Motion |
68%
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AIPMT - 1998
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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
Subtopic:  Linear SHM |
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Two simple harmonic motions of angular frequency 100 rad s -1 and 1000 rad ${s}^{-1}$ 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

Subtopic:  Linear SHM |
86%
From NCERT
NEET - 2008
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