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A particle of mass m is placed on a frictionless horizontal table and attached by two identical massless spicral springs of natural length b and stiffness k, to two fixed points A and B on the table. Points A and B are a distance 2a apart, where 2a>2b, so that the springs are stretched. The particle is then given a displacement along the line of the springs and released. Show that the motion that ensues is simple harmonic motion, and find its period.
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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