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A slender, uniform, metal rod with mass M is pivoted without friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring with force constant k is attached to the lower end of the rod, with the other end of the spring attached to a rigid support. If the rod is displaced by a small angle 0 from the vertical and released, show that it moves in angular SHM and calculate the period. (Hint: Assume that the angle 0 is small enough for the approximations sin 0 z 0 and cos 0 1 to be valid. The motion is d²0 simple harmonic if dt² + w²0 = 0, and the period is then T = 2 .)

A slender, uniform, metal rod with mass M is pivoted without friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring with force constant k is attached to the lower end of the rod, with the other end of the spring attached to a rigid support. If the rod is displaced by a small angle 0 from the vertical and released, show that it moves in angular SHM and calculate the period. (Hint: Assume that the angle 0 is small enough for the approximations sin 0 z 0 and cos 0 1 to be valid. The motion is d²0 simple harmonic if dt² + w²0 = 0, and the period is then T = 2 .)

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A slender, uniform, metal rod with mass M is pivoted without friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring with force constant k is attached to the lower end of the rod, with the other end of the spring attached to a rigid support. If the rod is displaced by a small angle 0 from the vertical and released, show that it moves in angular SHM and calculate the period. (Hint: Assume that the angle 0 is small enough for the approximations sin 0 2 0 and cos 0 2 1 to be valid. The motion is d²0 df2 simple harmonic if + @²0 = 0, and the period is 2л then T
Transcribed Image Text:A slender, uniform, metal rod with mass M is pivoted without friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring with force constant k is attached to the lower end of the rod, with the other end of the spring attached to a rigid support. If the rod is displaced by a small angle 0 from the vertical and released, show that it moves in angular SHM and calculate the period. (Hint: Assume that the angle 0 is small enough for the approximations sin 0 2 0 and cos 0 2 1 to be valid. The motion is d²0 df2 simple harmonic if + @²0 = 0, and the period is 2л then T
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