Vibrations of a body

Question

Describe with examples the undamped and damped vibrations.

Answer 1

Undamped and damped vibrations are two different types of oscillatory motion that occur in physical systems. Here's a description of each along with examples:

1. Undamped Vibrations: Undamped vibrations occur when a system oscillates freely without any energy dissipation or damping. In this case, once the system is set in motion, it will continue to oscillate indefinitely with constant amplitude and frequency. The energy of the system remains constant over time.

   Example: A simple pendulum swinging without any friction or air resistance is an example of undamped vibrations. Once the pendulum is set in motion, it will continue to swing back and forth at the same amplitude and frequency until external forces act upon it.

2. Damped Vibrations: Damped vibrations occur when a system's oscillations gradually decrease in amplitude over time due to the presence of damping forces. These damping forces dissipate the energy of the system, causing the oscillations to decay until the system comes to rest.

   Example: A mass-spring-damper system is a classic example of damped vibrations. When a mass is attached to a spring and immersed in a viscous fluid (creating damping), and then displaced from its equilibrium position, it will oscillate back and forth. However, due to damping, the amplitude of these oscillations gradually decreases until the mass comes to rest at its equilibrium position.