A. Based on a typical bond energy of 150 kBT and a typical bond length of 0.15 nm, use dimensional analysis to estimate the frequency of vibration of covalent bonds. b. Assume that the Lennard–Jones potential given by V(r)= a − b r12 r6 describes a covalent bond (though real covalent bonds are more appropriately described by alternatives such as the Morse potential that are not as convenient analytically). Using the typical bond energy as the depth of the potential and the typical bond length as its equilibrium position, find the parameters a and b. Do a Taylor expansion around this equilibrium position to determine the effective spring constant and the resulting typical frequency of vibration. c. Based on your results from (a) and (b), estimate the time step required to do a classical mechanical simulation of protein dynamics.