(a) Explanation Given information: The weight of the water bucket ( W ) is 7,000 lb. The distance between the helicopter and bucket ( L ) is 30 ft. The total stiffness of the cable in vertical direction ( k ) is 14000 lb / ft . The acceleration due to gravity ( g ) is 32.2 ft / s 2 . Calculation: Show the free body diagram of the weight as Figure (1). Take the moment about center O . ∑ M O = I G θ ¨ − m g L sin θ = m L 2 θ ¨ m L 2 θ ¨ + m g L sin θ = 0 m L ( L θ ¨ + g sin θ ) = 0 L θ ¨ + g sin θ = 0 θ ¨ + g L sin θ = 0 (1) The expression for the general differential equation as follows: θ ¨ + ω n 2 θ = 0 (2) Compare the equations (1) and (2) (b) To determine The frequency of oscillation in the vertical direction ( f n ) .

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Author: BEER

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…

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Chapter 19, Problem 19.160RP

(a)

To determine

The frequency of oscillation in the horizontal direction (fn).

(b)

To determine

The frequency of oscillation in the vertical direction (fn).

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Chapter 19, Problem 19.159RP

Chapter 19, Problem 19.161RP

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The frequency of oscillation in the horizontal direction ( f n ) .

Solution Summary: The author shows the free body diagram of the weight as Figure (1).

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The frequency of oscillation in the horizontal direction (fn).

The frequency of oscillation in the vertical direction (fn).

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Chapter 19 Solutions