Question

in damped vibration wavelength increases gradually with time ??????!!?

Answer 1

Free vibrations: When a body continues to oscillate with its own characteristics frequency. Such oscillations are known as free or natural vibrations of the body. Ideally, the body vibrates with its natural frequency for an indefinite time with a constant amplitude. Damped vibrations: In practice, the amplitude of vibrations decays with time and finally the body comes to rest at its mean position. So, we may conclude that there is a damping force on the vibrating body and this may be due to viscosity of the medium or other frictional forces. Such vibrations of decaying amplitude are referred to as resisted or damped vibrations. The motion of a simple pendulum is an example of a damped simple harmonic motion, because the amplitude gradually decreases with time and the bob finally comes to rest. Analytical treatment of damped vibrations: Let x be the displacement of a particle of mass m performing a damped motion from its initial position of rest. The following forces act on the body. (i) Restoring force (F1):