Consider a face-centered cubic monatomic bravais lattice in which each ion interacts only with its (twelve) nearest neighbors. assume that the interaction between a pair of neighboring ions is described by a pair potential depends only distance the pair of ions. show that the frequencies of the three normal modes with wave vector k are given by (a) a/m (22.960 where the are the eigenvalues of the 3 x 3 matrix: (22.97) here the sum is over the twelve nearest neighbors of r 0: (ty t z), (ti t r); (22.98) ow), and rr is the diadic formed from the unit vectors r r/r he, rr),v the constants a and b are: a 2g (d)/d, b 20p"(d) p'(d)/d], where

I'm kinda lost ! 1. when marilyn takes her pet dog for a walk, the dog walks at a veryconsistent pace of 0.55 m/s. draw a position-time graph to representmarilyn's dog walking the 19.8 m distance from the front of her house tothe nearest fire hydrant.2. both car a and car bleave school when a stopwatch reads zero. car atravels at a constant 75 km/h, and car b travels at a constant 85 km/h.a) draw a position-time graph showing the motion of both cars. howfar are the two cars from school when the stopwatch reads 2 hrs? calculate the distances and show them on your graph.b) both cars passed a gas station 120 km from the school. when dideach car pass the gas station? calculate the times and show themon your graph.3. the figure below shows the position-time graph showing a shopper'smovement up and down the aisle at a store.a) write a story describing the shopper's movements at the store.b) when does the shopper have a position of 6 m? c) how much time passes between when the shopper enters the aisleand when he gets to a position of 12 m? what is the shopper's averagevelocity between 37 s and 46 s?

Using the work energy theorem. what is the velocity of a 850kg car after starting at rest when 13,000j of work is done to it.

Atank has a shape of a cone with a radius at the top of 2 m and a height of 5 m. the tank also has a 1 m spout at the top of the tank. the tank is filled with water up to a height of 2 m. find the work needed to pump all the water out the top of the spout. (use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.)