Obtain an expression for the ratio of the average kinetic energy k to the average total energy e of the oscillator in terms of the dimensionless quantity ωo/ω. sketch this expression over an appropriate range of ω. for what value of ω are the average values of the kinetic and potential energies equal?

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)