(a) Explanation Given information: The sides of the equilateral triangular plate is b . The length of the wire is l . Calculation: The radius of the circumscribed circle in the equilateral triangle is b 3 Show the free body diagram of triangular plate and wire as in Figure (1). Calculate the angle ( ϕ ) using the relation: tan ϕ = Opposite side Adjacent side Substitute b θ 3 for opposite side and l for adjacent side. tan ϕ = b θ 3 l = b θ l 3 For small oscillation tan ϕ ≈ ϕ ϕ = b θ l 3 Write the expression for the force ( F ): F = T ϕ Substitute m g 3 for T and b θ l 3 for ϕ . F = m g 3 b θ l 3 Write the expression for moment of inertia ( I G ) at point G : I G = m b 2 12 Take moment about G in the system for external forces. ( ∑ M G ) e x t e r n a l = − F ( b 3 ) θ Substitute m g 3 b θ l 3 for F . ( ∑ M G ) e x t e r n a l = − ( m g 3 b θ l 3 ) ( b 3 ) θ = − m g b 2 9 l θ Take moment about G in the system for effective forces. ( ∑ M G ) e f f e c t i v e = I G θ ¨ Substitute m b 2 12 for I G (b) To determine The period ( τ ) of small oscillation of the plate when it is given a small horizontal displacement in a direction perpendicular to AB .

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Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 19.2, Problem 19.66P

(a)

To determine

The period (τ) of small oscillation of the plate when it is rotated through a small angle about a vertical axis through its mass center G.

(b)

To determine

The period (τ) of small oscillation of the plate when it is given a small horizontal displacement in a direction perpendicular to AB.

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Chapter 19.2, Problem 19.65P

Chapter 19.2, Problem 19.67P

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The period ( τ ) of small oscillation of the plate when it is rotated through a small angle about a vertical axis through its mass center G .

Solution Summary: The author shows the free body diagram of triangular plate and wire as in Figure (1).