Question

Quantum Phenomena are often negligible in the following “macroscopic” world examples. If we have a pendulum of 1 meter long with a mass 1-kg marble ball attached. Estimate the order of magnitude of the amplitude of the zero-point oscillation of this pendulum. Hint: zero-point oscillation is the lowest energy state. We discussed the sharing of the total energy between kinetic energy and potential energy.

Answer 1

from given data,total mechanical energy of the simple pendulum during the simple harmonic oscillations are, E = KE+PE = 5 mAv? +moAx? From Heisenberg Uncertinity principle, Ax. Ap = Ax (mdv) = Av=AAT Therefore, - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - For zero-point energy amplitude calculation (-2) samt tz (2ma? Ax ) = 0 Ax= [4 ima] Here, 5 NDO 001 9.8 m/s V 1.0m = 3.13rad's Therefore amplitude of oscillations are, (6.626x10-34J.s) Ax=1 47(1.0kg)(3.13rad's) =0.203x10m - 2.03x10 m (or) 2.03 nm