Question:
Distinguish between free vibrations and forced vibrations (Two points).
Distinguish between free vibrations and forced vibrations (Two points).
Show Hint
In free vibrations, the system oscillates at its own natural frequency, while in forced vibrations, the system is forced to vibrate at the frequency of the applied external force.
Updated On: Oct 27, 2025
Hide Solution
Verified By Collegedunia
Solution and Explanation
Step 1: Free Vibrations.
Free vibrations occur when a body or system vibrates without any external force acting on it, after an initial displacement. The system vibrates at its natural frequency, and the amplitude of vibration decreases over time due to damping forces like friction or air resistance.
Step 2: Forced Vibrations.
Forced vibrations happen when an external force is applied to a system, causing it to vibrate at the frequency of the external force. In this case, even if the system has a natural frequency, the external force dominates and dictates the vibration frequency.
Free vibrations occur when a body or system vibrates without any external force acting on it, after an initial displacement. The system vibrates at its natural frequency, and the amplitude of vibration decreases over time due to damping forces like friction or air resistance.
Step 2: Forced Vibrations.
Forced vibrations happen when an external force is applied to a system, causing it to vibrate at the frequency of the external force. In this case, even if the system has a natural frequency, the external force dominates and dictates the vibration frequency.
Was this answer helpful?
0
0
Top Questions on Vibrations
- The equation of free vibration of a system is \( X + 36\pi^2 X = 0 \). Its natural frequency is:
- The dynamic response amplitude \( |H(\omega)| \) of a single degree of freedom system subjected to support motion is given by the following expression: \[ |H(\omega)| = \sqrt{\frac{1 + 4 \zeta^2 \left( \frac{\omega}{\omega_n} \right)^2 }{\left[ 1 - \left( \frac{\omega}{\omega_n} \right)^2 \right]^2 + 4 \zeta^2 \left( \frac{\omega}{\omega_n} \right)^2} } \] Where the damping ratio is \( \zeta \), the excitation frequency is \( \omega \), and the natural frequency of the system is \( \omega_n \). The amplitude \( |H(\omega)| \) increases with an increase in damping ratio (\( \zeta \)) if the excitation frequency (\( \omega \)) is ________ the natural frequency (\( \omega_n \)) of the system.
- A single degree of freedom system is undergoing free oscillation. The natural frequency and damping ratio of the system are \(1 \, {rad/sec}\) and \(0.01\) respectively.
The reduction in peak amplitude over three cycles is ________ % (rounded off to one decimal place). - The fundamental frequency of a string of length \( l \) is \( n \). The string is cut into 3 parts \( l_1, l_2, \) and \( l_3 \), each having fundamental frequency \( n_1, n_2, n_3 \). Then, what is the relationship between \( n_1, n_2, n_3 \)?
- KEAM - 2025
- Physics
- Vibrations
A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness \( k = 100 \, {N/m} \), as shown in the figure. The natural frequency of free vibration of the system is _____________ rad/s (answer in integer).
- GATE AE - 2025
- Structures
- Vibrations
View More Questions
Questions Asked in Maharashtra Class XII exam
- Write short notes: British East India Company:
- Maharashtra Class XII - 2025
- European Imperialism
- State the formula for magnetic induction produced by a current in a circular arc of a wire. Hence find the magnetic induction at the centre of a current carrying circular loop.
- Maharashtra Class XII - 2025
- Magnetic Field due to a Current Element
- Prepare an ‘Appeal’ on the topic ‘Women’s Security and Safety’ with the help of the following points: (100/150 words)
— Respect women’s rights
— Safety measures and support systems
— Collective responsibility
— Government initiatives
- Maharashtra Class XII - 2025
- Writing Skills
- Answer the following questions: % Question (i) Write the negation of the statement: \( \exists n \in \mathbb{N} \) such that \( n + 8 > 11 \).
- Maharashtra Class XII - 2025
- Quantifiers and Negation
- Derive the relation between half life and rate constant for a first order reaction.
- Maharashtra Class XII - 2025
- Chemical Kinetics
View More Questions