(a) Explanation Given Information: The period ( τ n ) of the vertical plane is 1.5 sec. The maximum velocity ( v m ) of the bob is 0.5 m/s . The acceleration due to gravity ( g ) value is 9.81 m/s 2 . Calculation: Write the expression for the period ( τ n ) : τ n = 2 π ω n Here, ω n is the natural circular frequency. Rewrite the above equation for ω n . ω n = 2 π τ n (1) Calculate the natural circular frequency ( ω n ) : Substitute 1.5 sec for τ n in Equation (1). ω n = 2 π 1.5 = 4.1888 rad/s Show the simple pendulum with maximum amplitude and length as in Figure (1): Write the expression for angle ( θ ) : θ = θ m sin ( ω n t + ϕ ) (2) Differentiate the above equation. θ ˙ = θ m ω n cos ( ω n t + ϕ ) (3) The angle ( θ ) is 0 at time( t ) is 0. Substitute 0 for t and 0 for θ in equation (2). 0 = θ m sin ( ω n ( 0 ) + ϕ ) ϕ = 0 Substitute 0 for ϕ and 0 for t in equation (3) and rewrite the equation for maximum angular velocity ( θ ˙ m ) (b) To determine The maximum tangential acceleration ( a t ) m of the bob.

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ISBN: 9781260265453

Author: BEER

Publisher: MCG

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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 19.1, Problem 19.7P

(a)

To determine

The amplitude (θm) of the motion in degrees.

(b)

To determine

The maximum tangential acceleration (at)m of the bob.

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Chapter 19.1, Problem 19.6P

Chapter 19.1, Problem 19.8P

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The amplitude ( θ m ) of the motion in degrees.

Solution Summary: The author explains how the amplitude of the motion in degrees is underset_12.23°.

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The amplitude (θm) of the motion in degrees.

The maximum tangential acceleration (at)m of the bob.

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Chapter 19 Solutions