(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: 9781260663778

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…

Question

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