5. Imagine an anti-yıavily fuice lhal acts just like Newtonian gravity, but repels. So in the diagram, M1 repels the little mass, m, with a force magnitude of Fanti-grav = GM;m/r12 , where G still equals 6.674 x 10-11 m3kg1s 2, M, = M M2 = --- %3D -a +a 'x(t) The system shown in the diagram is isolated. M1 and M2 each repel m. No other forces act on m. And M, and M2 are held in place at ±a. d Write an expression for the restoring force exerted onto m. The expression should be in terms of G, M, m, a and x(t).

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Chapter7: Gravitation
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Problem 98A
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Imagine an anti-yravily fuice lhal acts
just like Newtonian gravity, but repels. So in the
5.
M,
M2 = M
= M
diagram, M1 repels the little mass, m, with a force
magnitude of Fanti-grav = GM,m/r12, where G still
-12
+a
-a
equals 6.674 x 1011 m3kg-1s2,
'x(t)
The system shown in the diagram is isolated. M1 and M2 each repel m. No other
forces act on m. And M, and M2 are held in place att a.
sho an expression for the restoring force exerted onto m. The expression
should be in terms of G, M, m, a and x(t).
b. Is the motion of the little mass, m, simple harmonic motion?
Explain why or why not.
c. Determine the period for small amplitude (x << a) oscillations of m. Leave your
answer in terms of G, M and a.
Transcribed Image Text:Imagine an anti-yravily fuice lhal acts just like Newtonian gravity, but repels. So in the 5. M, M2 = M = M diagram, M1 repels the little mass, m, with a force magnitude of Fanti-grav = GM,m/r12, where G still -12 +a -a equals 6.674 x 1011 m3kg-1s2, 'x(t) The system shown in the diagram is isolated. M1 and M2 each repel m. No other forces act on m. And M, and M2 are held in place att a. sho an expression for the restoring force exerted onto m. The expression should be in terms of G, M, m, a and x(t). b. Is the motion of the little mass, m, simple harmonic motion? Explain why or why not. c. Determine the period for small amplitude (x << a) oscillations of m. Leave your answer in terms of G, M and a.
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