If $$x = 5 \mathrm {sin }\left(\pi t+ {\dfrac {\pi} 3}\right)~\text m$$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively are:
1. $$5~\text m, 2~\text s$$
2. $$5~\text {cm}, 1~\text s$$
3. $$5~\text m, 1~\text s$$
4. $$5~\text {cm}, 2~\text s$$
Subtopic:  Simple Harmonic Motion |
68%
From NCERT
NEET - 2024
Hints

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $$\dfrac{x}{2}$$ times its original time period. Then the value of $$x$$ is:
1. $$\sqrt2$$
2. $$2\sqrt3$$
3. $$4$$
4. $$\sqrt3$$
Subtopic:  Angular SHM |
64%
From NCERT
NEET - 2024
Hints

If $$T_1,T_2,T_3,T_4$$ and $$T_5$$ represent the tension in the string of a simple pendulum when the bob is at the left extreme, right extreme, mean, any intermediate left and any intermediate right positions, respectively. Then which of the following relations are correct?
 (A) $$T_1=T_2$$ (B) $$T_3>T_2$$ (C) $$T_4>T_3$$ (D) $$T_5>T_2$$
Choose the most appropriate answer from the options given below:
 1 (A), (B) and (C) only 2 (B), (C) and (D) only 3 (A), (B) and (E) only 4 (C), (D) and (E) only
Subtopic:  Simple Harmonic Motion |
61%
From NCERT
NEET - 2024
Hints

A particle executing simple harmonic motion with amplitude $$A$$ has the same potential and kinetic energies at the displacement:
 1 $$2\sqrt{A}$$ 2 $$\dfrac{A}{2}$$ 3 $$\dfrac{\mathrm{A}}{\sqrt{2}}$$ 4 $$A\sqrt{2}$$
Subtopic:  Energy of SHM |
78%
From NCERT
NEET - 2024
Hints

The two-dimensional motion of a particle, described by $$\overrightarrow{\mathbf{r}}=\begin{pmatrix}\hat{i}+2\hat{j}\end{pmatrix} A\cos\omega t$$ is a/ an:
A. parabolic path
B. elliptical path
C. periodic motion
D. simple harmonic motion
Choose the correct answer from the options given below:
 1 B, C, and D only 2 A, B, and C only 3 A, C, and D only 4 C and D only
Subtopic:  Types of Motion |
From NCERT
NEET - 2024
Hints

The $$x\text-t$$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $$t=2$$ s is:

 1 $$-\dfrac{\pi^2}{16} ~\text{ms}^{-2}$$ 2 $$\dfrac{\pi^2}{8}~ \text{ms}^{-2}$$ 3 $$-\dfrac{\pi^2}{8} ~\text{ms}^{-2}$$ 4 $$\dfrac{\pi^2}{16} ~\text{ms}^{-2}$$
Subtopic:  Simple Harmonic Motion |
60%
From NCERT
NEET - 2023
Hints

A simple pendulum oscillating in air has a period of $$\sqrt3$$ s. If it is completely immersed in non-viscous liquid, having density $$\left(\dfrac14\right)^{\text{th}}$$ of the material of the bob, the new period will be:
 1 $$2\sqrt3$$ s 2 $$\dfrac{2}{\sqrt3}$$ s 3 $$2$$ s 4 $$\dfrac{\sqrt 3}{2}$$ s
Subtopic:  Angular SHM |
From NCERT
NEET - 2023
Hints

Two pendulums of length $$121$$ cm and $$100$$ cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:
 1 $$8$$ 2 $$11$$ 3 $$9$$ 4 $$10$$
Subtopic:  Angular SHM |
67%
From NCERT
NEET - 2022
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During simple harmonic motion of a body, the energy at the extreme position is:

 1 both kinetic and potential 2 is always zero 3 purely kinetic 4 purely potential
Subtopic:  Energy of SHM |
78%
From NCERT
NEET - 2022
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Identify the function which represents a non-periodic motion?
 1 $$e^{-\omega t}$$ 2 $$\text{sin}\omega t$$ 3 $$\text{sin}\omega t+\text{cos}\omega t$$ 4 $$\text{sin}(\omega t+\pi/4)$$
Subtopic:  Types of Motion |
81%
From NCERT
NEET - 2022
To view explanation, please take trial in the course.
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