Amass m fixed to a spring oscillates between limits −a ≤ x ≤ a subject to hooke’s law f = −mω2 x . as it moves back and forth, you take many photographs at random intervals. on each picture you measure the distance the mass has moved. a. find the probability density ρ(x) for finding the mass is at a position x in a random picture. b. sketch ρ(x) and interpret the result. where is ρ(x) largest and where is it smallest? c. what is the average position of the mass? explain your result. d. what is the standard deviation from the mean of the mass? e. how does your result for part d compare to a uniform motion at constant speed in the range −a ≤ x ≤ a ? explain why this makes sense.