Two point masses m are held in place a distance d apart. Another point mass M is midway between them. M is then displaced a small distance x perpendicular to the line connecting the two fixed masses and released.
(a) Show that the magnitude of the net gravitational force on M due to the fixed masses is given apprmumate1 y by F, 16GmMx/d3 if x « d. What <(b) Show that the mass M will oscillate with an angular frequency of (4/d) Y Gm/d and period wd/2, Id/Gm.
(c) What would the period be if m = 100 kg and d = 25.0 cm? Does it seem that you could easily measure this period? What things prevent this experiment from easily being performed in an ordinary physics lab? (
d) Will M oscillate if it is displaced from the center a small distance x toward earlier of the fixed masses? Why?