The motion of a simple pendulum executing S.H.M. is represented by the following equation. y = A sin(πt + φ), where time is measured in second. The length of pendulum is
- 97.23 cm
- 25.3 cm
- 99.4 cm
- 406.1 cm
The Correct Option is C
Solution and Explanation
The correct answer is (C) : 99.4 cm
During the time period of SHM,
\(T=2π\sqrt{\frac{l}{g}} and ω = \frac{2π}{T}\)
Hence, \(ω=\frac{2π}{2π}\sqrt{\frac{g}{l}}\)
\(ω=\sqrt{\frac{g}{l}}\)
\(l=\frac{g}{ω^2}\)
By comparing the equation , we get
ω=π
Therefore ,
\(l = \frac{g}{π^2} ≈ 99.4 cm\)
Top Questions on 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
- T² vs l graph represents:
- UPCATET - 2025
- Physics
- simple harmonic motion
- What is the time taken by a particle executing SHM with a time period \( T \) sec from a positive extreme position to half of the amplitude?
- UPCATET - 2025
- Physics
- simple harmonic motion
- A particle executes SHM with amplitude \( A \) and time period \( T \). The time taken to move from equilibrium to \( \frac{A}{2} \) is:
- AP EAPCET - 2025
- Physics
- simple harmonic motion
- A 1.5 kg block is placed on a frictionless surface and attached to a spring with a spring constant of 100 N/m. If the block is displaced by 0.2 m from its equilibrium position, what is the potential energy stored in the spring?
- MHT CET - 2025
- Physics
- simple harmonic motion
Questions Asked in JEE Main exam
A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in the figure. Initially, by applying horizontal velocity \(v_0\) at the point ‘A’, the string becomes slack when the bob reaches at the point ‘D’. The ratio of the kinetic energy of the bob at the points B and C is:
- JEE Main - 2025
- Kinetic Energy
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
- JEE Main - 2025
- permutations and combinations
- A bar magnet has total length \( 2l = 20 \) units and the field point \( P \) is at a distance \( d = 10 \) units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then the uncertainty of the magnetic field at point P is:
- JEE Main - 2025
- Magnetic Field
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
- JEE Main - 2025
- Relations and functions
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