Period of Oscillation of a Meter Stick & Piston at Maximum Speed
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A uniform meter stick swings about a pivot point which is a distance x = 27.4 cm from the end of the stick. What is its period of oscillation?
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The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 0.66 m. If the piston moves with simple harmonic motion with an angular frequency of 180 rev/min, what is its maximum speed?
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This solution helps with physics question about meter stick period of oscillation and piston maximum speed.
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A uniform meter stick swings about a pivot point which is a distance x = 27.4 cm from the end of the stick. What is its period of oscillation?
Solution:
Weight mg of the meter stick acts vertically down at its centre of gravity.
Torque acting on the meter stick about the pivot = τ = Force mg x Perpendicular distance of the line of action of the force from the pivot = mg x 0.226sinθ
For small displacement sinθ ≈ θ. Hence, τ = mg x 0.226 θ = m x 9.8 x 0.226 x θ = 2.215m θ
As the ...
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