A Pivoting Rod on a Spring – (full respect) help..
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Question “A Pivoting Rod on a Spring – (full respect) help..”
A slender, uniform metal rod of mass and length is pivoted without friction about an axisthrough its midpoint and perpendicularto the rod. A horizontalspring, assumed massless and with force constant , is attached to the lower end of the rod, withthe other end of the spring attached to a rigid support.
(a) We start by analyzing the torques acting on the rod when it isdeflected by a small angle from the vertical. Considerfirst the torque due to gravity. Which of the following statementsmost accurately describes the effectof gravity on the rod?
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(b) Find the torque due to the spring. Assume that is small enough that the springremains effectively horizontal andyou can approximate (and).Express the torque as a function of and other parametersofthe problem.
(c) What is the angular frequency of oscillations ofthe rod?Express the angular frequency interms of parameters given in the introduction.
Thanks
Answer
Answer 1
Diagram:
Consider that the metal rod’s mass is = MThe rod’s length is = LThe rod’s x-componenet force is
Where x =L/2 sinthso.
The torque
=
We also know this.
The angular frequencyis
The time period is
This may be of assistance to you
Answer 2
A. The rod is not subject to torque from gravity.
B. -k*th* (L/2)
2
C.
(3k/M)=sqar(3k/m)
Conclusion
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