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Question 2: Oscillating Beam A rigid beam of mass M and length L is supported by one wire as shown. The beam is attached to a hinge at point P. The wire has cross-section A and Young's modulus Y. In static equilibrium the wire is under a tension T. Assume that in equilibrium the wire makes an angle of $\pi$/2 with the wall. h PK L a) Suppose the pole is rotated about the pivot point P away from its equilibrium orientation by an arbitrary clockwise angle $\alpha$. From the net torque equation, find the the equilibrium torque equation about point P. You can leave your answer in terms of the tension in the wire, T, h, L, M, g, and the equilibrium angle between the wall and the poll $\theta_0$. b) Calculate the frequency of small oscillations that the beam will execute if perturbed from equilibrium. Ignore bending of the beam. c) Using your result from part (b), infer what the frequency of small oscillations would be is you two wires were connected to the beam in the same configuration as the single wire you analyzed above. for one wire take: h = $h_1$, A = $A_1$,and Y = $Y_1$. For the second wire take: h = $h_2$, A = $A_2$,and Y = $Y_2$.

          Question 2: Oscillating Beam
A rigid beam of mass M and length L is supported by one wire as shown. The beam is attached to a hinge at
point P. The wire has cross-section A and Young's modulus Y. In static equilibrium the wire is under a tension
T. Assume that in equilibrium the wire makes an angle of $\pi$/2 with the wall.
h
PK
L
a) Suppose the pole is rotated about the pivot point P away from its equilibrium orientation by an arbitrary
clockwise angle $\alpha$. From the net torque equation, find the the equilibrium torque equation about point P. You can
leave your answer in terms of the tension in the wire, T, h, L, M, g, and the equilibrium angle between the wall
and the poll $\theta_0$.
b) Calculate the frequency of small oscillations that the beam will execute if perturbed from equilibrium. Ignore
bending of the beam.
c) Using your result from part (b), infer what the frequency of small oscillations would be is you two wires were
connected to the beam in the same configuration as the single wire you analyzed above. for one wire take: h = $h_1$,
A = $A_1$,and Y = $Y_1$. For the second wire take: h = $h_2$, A = $A_2$,and Y = $Y_2$.

Question 2: Oscillating Beam
A rigid beam of mass M and length L is supported by one wire as shown. The beam is attached to a hinge at
point P. The wire has cross-section A and Young's modulus Y. In static equilibrium the wire is under a tension
T. Assume that in equilibrium the wire makes an angle of π/2 with the wall.
h
PK
L
a) Suppose the pole is rotated about the pivot point P away from its equilibrium orientation by an arbitrary
clockwise angle α. From the net torque equation, find the the equilibrium torque equation about point P. You can
leave your answer in terms of the tension in the wire, T, h, L, M, g, and the equilibrium angle between the wall
and the poll θ0.
b) Calculate the frequency of small oscillations that the beam will execute if perturbed from equilibrium. Ignore
bending of the beam.
c) Using your result from part (b), infer what the frequency of small oscillations would be is you two wires were
connected to the beam in the same configuration as the single wire you analyzed above. for one wire take: h = h1,
A = A1,and Y = Y1. For the second wire take: h = h2, A = A2,and Y = Y2.

Added by George O.

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