Question

A student thinks that any real vibration must be damped. Is the student correct? If so, give convincing reasoning. If not, give an example of a real vibration that keeps constant amplitude forever if the system is isolated.

Short answer

The students die down eventually as their energy transferring to their surroundings, mostly everyday vibrations are damped. The atoms in the molecules do not damp out and they have modes of vibration.

Step-by-step solution

The potential energy

Potential energy for an object of mass m oscillating at the end of a spring of force constant k varies with time and are given by

$U=\frac{1}{2}k{x}^2=\frac{1}{2}k{A}^2{\cos }^2\left(\omega t+\varphi \right)$

The total energy of a simple harmonic oscillator is a constant of the motion and is given by

$E=\frac{1}{2}k{x}^2$

Find the reasoning

The students die down eventually as their energy transferring to their surroundings, mostly everyday vibrations are damped. The atoms in the molecules do not damp out and they have modes of vibration.