A coin with a mass of 8.31 g suspended on a rubber band has a vibrational frequency of . Calculate (a) the force constant of the rubber band, (b) the zero point energy, (c) the total vibrational energy if the maximum displacement is 0.725 cm, and (d) the vibrational quantum number corresponding to the energy in part (c).

Determine the maximum r-value of the polar equation r =3+3 cos 0

Total solidification times of three casting geometries are to be compared: a sphere, a cylinder, in which the length-to-diameter ration - 1.0, and a cube. volume = 1000 cm^3 for all three shhapes, and the same casting alloy is used. a) determine the solidification times of each geometry b) based on the results of part (a), which geometric element would make the best riser? c) if the mold constant = 3.5 min/cm^2 in chvorinov's rule, compute the total solidification time for each casting.

The radius of an atom is closest in size to a