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Unformatted text preview: ained to move along the x-axis, shown as a dashed line. (Let x = 0 represent the point on
the axis directly between the spheres, with +x to the right.) Figure 3:
(a) Compute the net force on the ball by both large spheres, and write down a diﬀerential equation that
governs the motion of the small ball.
(b) Is the net force exerted on the small ball a restoring force? Explain how you can tell from your
diﬀerential equation above? Under what limiting conditions for x is it possible to say that the motion
of the mass m can be approximated as simple harmonic motion? (For large x? For small x? Large or
small compared to what?) In this limiting case, determine an expression for the period of motion in
terms of the given parameters. Explain your reasoning. CONTINUED –3– PHYS 2210 6. An ideal (massless) spring with force constant k is used to hang a crate from the ceiling, as shown (left,
below). Suppose that the spring were treated as two separate springs (1 and 2) connected end-to-end. (See
Figure) Treat each spring as having its own spring constant (k1 or k2 ) given...
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