The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is $2s$. The period of oscillation of the same pendulum on the planet would be :
- $\frac{2}{\sqrt{3}} s$
- $2 \sqrt{3} s$
- $\frac{\sqrt{3}}{2} s$
- $\frac{3}{2} s $
The Correct Option is B
Solution and Explanation
Top Questions on 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
- 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
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
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
- A simple pendulum performing small oscillations at a height R above Earth's surface has a time period of \(T_1 = 4\) s. What would be its time period at a point which is at a height \(2R\) from Earth's surface?
- BITSAT - 2025
- Physics
- simple harmonic motion
Questions Asked in JEE Main exam
Given below are two statements:
Statement (I):
are isomeric compounds.
Statement (II):
are functional group isomers.
In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2025
- Isomerism
- Two projectiles are fired with the same initial speed from the same point on the ground at angles of \( (45^\circ - \alpha) \) and \( (45^\circ + \alpha) \), respectively, with the horizontal direction. The ratio of their maximum heights attained is:
- JEE Main - 2025
- Fluid Mechanics
Given below are two statements: one is labelled as Assertion \(A\) and the other as Reason \(R\):
Assertion \(A\): A sound wave has higher speed in solids than in gases.
Reason \(R\): Gases have higher value of Bulk modulus than solids.- JEE Main - 2025
- Fluid Mechanics
- Consider the following statements: Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface of a liquid. As the temperature of liquid rises, the coefficient of viscosity increases. As the temperature of gas increases, the coefficient of viscosity increases. The onset of turbulence is determined by Reynolds number. In a steady flow, two streamlines never intersect. Choose the correct answer from the options given below:
- JEE Main - 2025
- Fluid Mechanics
In the experiment for measurement of viscosity \( \eta \) of a given liquid with a ball having radius \( R \), consider following statements:
A. Graph between terminal velocity \( V \) and \( R \) will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of \( \eta \) will change.- JEE Main - 2025
- Fluid Mechanics
Concepts Used:
Simple Harmonic Motion
Simple Harmonic Motion is one of the most simple forms of oscillatory motion that occurs frequently in nature. The quantity of force acting on a particle in SHM is exactly proportional to the displacement of the particle from the equilibrium location. It is given by F = -kx, where k is the force constant and the negative sign indicates that force resists growth in x.
This force is known as the restoring force, and it pulls the particle back to its equilibrium position as opposing displacement increases. N/m is the SI unit of Force.
Types of Simple Harmonic Motion
Linear Simple Harmonic Motion:
When a particle moves to and fro about a fixed point (called equilibrium position) along with a straight line then its motion is called linear Simple Harmonic Motion. For Example spring-mass system
Conditions:
The restoring force or acceleration acting on the particle should always be proportional to the displacement of the particle and directed towards the equilibrium position.
- – displacement of particle from equilibrium position.
- – Restoring force
- - acceleration
Angular Simple Harmonic Motion:
When a system oscillates angular long with respect to a fixed axis then its motion is called angular simple harmonic motion.
Conditions:
The restoring torque (or) Angular acceleration acting on the particle should always be proportional to the angular displacement of the particle and directed towards the equilibrium position.
Τ ∝ θ or α ∝ θ
Where,
- Τ – Torque
- α angular acceleration
- θ – angular displacement