Imagine an anti-yravily fuice lhal acts M1 5. 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/r,2, where G still equals 6.674 x 10-11 m³kg1s2. M2 = M 2 = M --- +a -a (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 t a. a, shte 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 you answer in terms of G, M and a.

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Chapter7: Gravitation
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Problem 98A
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Imagine an anti-yravily fuice lhal acls
just like Newtonian gravity, but repels. So in the
5.
M1
M2
= M
= M
diagram, M1 repels the little mass, m, with a force
magnitude of Fanti-grav = GM,m/r,2, where G still
2
+a
---
-a
equals 6.674 x 10-11 m³kg1s2.
(t)
The system shown in the diagram is isolated. M, and M2 each repel m. No other
forces act on m. And M, and M2 are held in place at ± a.
a,
vrite 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.
pyright 2022 D.Loranz, All Rights Reserved
Transcribed Image Text:Imagine an anti-yravily fuice lhal acls just like Newtonian gravity, but repels. So in the 5. M1 M2 = M = M diagram, M1 repels the little mass, m, with a force magnitude of Fanti-grav = GM,m/r,2, where G still 2 +a --- -a equals 6.674 x 10-11 m³kg1s2. (t) The system shown in the diagram is isolated. M, and M2 each repel m. No other forces act on m. And M, and M2 are held in place at ± a. a, vrite 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. pyright 2022 D.Loranz, All Rights Reserved
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