A particle oscillates in simple harmonic motion such that its speed and acceleration at distance 2 m from mean position are 4 m/s and 16 m/s2 respectively. Find the amplitude of oscillation of the particle.
- √10 m
- √6 m
- √8 m
- √3 m
The Correct Option is B
Solution and Explanation
Top Questions on simple harmonic motion
A particle is subjected to simple harmonic motions as: $ x_1 = \sqrt{7} \sin 5t \, \text{cm} $ $ x_2 = 2 \sqrt{7} \sin \left( 5t + \frac{\pi}{3} \right) \, \text{cm} $ where $ x $ is displacement and $ t $ is time in seconds. The maximum acceleration of the particle is $ x \times 10^{-2} \, \text{m/s}^2 $. The value of $ x $ is:
- JEE Main - 2025
- Physics
- simple harmonic motion
Two simple pendulums having lengths $l_{1}$ and $l_{2}$ with negligible string mass undergo angular displacements $\theta_{1}$ and $\theta_{2}$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?
- JEE Main - 2025
- Physics
- simple harmonic motion
- Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Knowing initial position \( x_0 \), and initial momentum \( p_0 \) is enough to determine the position and momentum at any time \( t \) for a simple harmonic motion with a given angular frequency \( \omega \).
Reason (R): The amplitude and phase can be expressed in terms of \( x_0 \) and \( p_0 \).
In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2025
- Physics
- simple harmonic motion
- A particle is executing simple harmonic motion with a time period of 2 s and amplitude 1 cm. If \( D \) and \( d \) are the total distance and displacement covered by the particle in 12.5 s, then the ratio \( \frac{D}{d} \) is:
- JEE Main - 2025
- Physics
- simple harmonic motion
- At 27°C temperature, the mean kinetic energy of the atoms of an ideal gas is \( E_1 \). If the temperature is increased to 327°C, then the mean kinetic energy of the atoms will be
- KCET - 2025
- Physics
- simple harmonic motion
Questions Asked in JEE Main exam
- For two identical cells each having emf \(E\) and internal resistance \(r\), the current through an external resistor of \(6\,\Omega\) is the same when the cells are connected in series as well as in parallel. The value of the internal resistance \(r\) is ________ \(\Omega\).
- JEE Main - 2026
- Current electricity
- For three unit vectors \( \vec a, \vec b, \vec c \) satisfying \[ |\vec a-\vec b|^2 + |\vec b-\vec c|^2 + |\vec c-\vec a|^2 = 9 \] and \[ |2\vec a + k\vec b + k\vec c| = 3, \] the positive value of \( k \) is:
- JEE Main - 2026
- Vector Algebra
In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$)
- JEE Main - 2026
- Rotational Mechanics
- The system of linear equations
$x + y + z = 6$
$2x + 5y + az = 36$
$x + 2y + 3z = b$
has- JEE Main - 2026
- Matrices and Determinants
Method used for separation of mixture of products (B and C) obtained in the following reaction is:
- JEE Main - 2026
- p -Block Elements