(a) Explanation Given Information: The cord length ( l ) of the simple pendulum is 40 in . . The angle ( θ ) at rest is + 5 ° . The acceleration due to gravity ( g ) value is 32.2 ft/s 2 . Calculation: Calculate the natural circular frequency ( ω n ) using the relation: ω n = g l Substitute 32.2 ft/s 2 for g and 40 in . for l . ω n = 32.2 ( 40 in . × 1 ft 12 in . ) = 9.66 = 3.1081 rad/s Write the expression for angle displacement ( θ ) : θ = θ m sin ( ω n t + ϕ ) (1) Differentiate the above equation. θ ˙ = θ m ω n cos ( ω n t + ϕ ) (2) At time ( t ) 0 sec a the angle displacement ( θ ) is + 5 ° and the angular velocity ( θ ˙ ) is 0 (b) To determine The magnitude of the velocity ( v ) and acceleration ( a ) of the bob.

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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…

Question

Chapter 19.1, Problem 19.13P

(a)

To determine

The angle (θ) the bob released after (t) 1.6 sec.

(b)

To determine

The magnitude of the velocity (v) and acceleration (a) of the bob.

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Chapter 19.1, Problem 19.12P

Chapter 19.1, Problem 19.14P

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The angle ( θ ) the bob released after ( t ) 1.6 sec.

Solution Summary: The author calculates the natural circular frequency using the relation: stackreldottheta.

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The angle (θ) the bob released after (t) 1.6 sec.

The magnitude of the velocity (v) and acceleration (a) of the bob.

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Chapter 19 Solutions