A spring is stretched by 5 cm by a force of 10 N. The time period of the oscillations, when a mass of 2 kg is suspended by it, is
0.628 s
0.0628 s
6.28 s
3.14 s
The Correct Option is A
Solution and Explanation
To solve this problem, we need to determine the time period of oscillation for a mass suspended from a spring. The force required to stretch the spring is given, as well as the mass attached.
Start by understanding Hooke's Law, which states that the force \(F\) needed to extend or compress a spring by distance \(x\) is proportional to that distance. It can be described as:
\(F = kx\)
Where:
- \(F = 10 \, \text{N}\): Force applied to the spring.
- \(x = 0.05 \, \text{m}\): Extension length of the spring, converted from centimeters to meters.
- \(k\) is the spring constant we are looking to find.
Rearranging Hooke’s Law gives us:
\(k = \frac{F}{x} = \frac{10}{0.05} = 200 \, \text{N/m}\)
Now, using the formula for the time period \(T\) of a mass-spring system:
\(T = 2\pi \sqrt{\frac{m}{k}}\)
Where:
- \(m = 2 \, \text{kg}\): Mass attached to the spring.
- \(k = 200 \, \text{N/m}\): Spring constant.
Substituting these values in gives:
\(T = 2\pi \sqrt{\frac{2}{200}} = 2\pi \sqrt{0.01} = 2\pi \times 0.1 = 0.628 \, \text{s}\)
Thus, the correct time period of oscillation is 0.628 seconds, which matches the given correct answer.
Top Questions on Waves and Oscillations
- The displacement of a particle executing simple harmonic motion with time period \(T\) is expressed as \[ x(t)=A\sin\omega t, \] where \(A\) is the amplitude of oscillation. If the maximum value of the potential energy of the oscillator is found at \[ t=\frac{T}{2\beta}, \] then the value of \(\beta\) is ________.
- JEE Main - 2026
- Physics
- Waves and Oscillations
Using a variable frequency ac voltage source the maximum current measured in the given LCR circuit is 50 mA for V = 5 sin (100t) The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is_______ µF.
- JEE Main - 2026
- Physics
- Waves and Oscillations
- A cylindrical block of mass $M$ and area of cross section $A$ is floating in a liquid of density $\rho$ with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is ___.
- JEE Main - 2026
- Physics
- Waves and Oscillations
- Using a simple pendulum experiment $g$ is determined by measuring its time period $T$. Which of the following plots represent the correct relation between the pendulum length $L$ and time period $T$?
- JEE Main - 2026
- Physics
- Waves and Oscillations
- A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x(t) = \alpha t^2 + \beta t + \gamma$ m, where $\alpha = 1$ m/s$^2$, $\beta = 1$ m/s and $\gamma = 1$ m. The work done on the body during the time interval $t = 2$ s to $t = 3$ s, is _________ J.
- JEE Main - 2026
- Physics
- Waves and Oscillations
Questions Asked in NEET exam
- Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y. She notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.
- NEET (UG) - 2025
- Relative Velocity
- A physical quantity P is related to four observations a, b, c, and d as follows: P = a3 b2 (c / √d) The percentage errors of measurement in a, b, c, and d are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity P is:
- NEET (UG) - 2025
- Dimensional analysis and its applications
What is Microalbuminuria ?
- NEET (UG) - 2025
- Human physiology
The output (Y) of the given logic implementation is similar to the output of an/a …………. gate.
- NEET (UG) - 2025
- Logic gates
- An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature \(27^\circ\)C. The mass of the oxygen withdrawn from the cylinder is nearly equal to: [Given, \(R = \frac{100}{12} \text{ J mol}^{-1} \text{K}^{-1}\), and molecular mass of \(O_2 = 32 \text{ g/mol}\), 1 atm pressure = \(1.01 \times 10^5 \text{ N/m}^2\)]
- NEET (UG) - 2025
- Ideal-gas equation and absolute temperature
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