Explanation Given information: The mass ( m ) of the bar is 3.6 kg. The length ( l ) of the bar is 750 mm. Assume the acceleration due to gravity ( g ) as 9.81 m/s 2 . Calculation: Show the position of displacement as in Figure (1). For position 1: Write the expression for mass moment of inertia rod ( I ): I = ( m l 2 3 ) Write the expression the velocity ( v m ) of bar: v m = l θ ˙ Write the expression for the kinetic energy ( T 1 ) : T 1 = 1 2 m v m 2 + 2 ( 1 2 I θ ˙ 2 ) Substitute ( m l 2 3 ) for I and l θ ˙ for v m . T 1 = 1 2 m ( l θ ˙ ) 2 + 2 ( 1 2 ( m l 2 3 ) θ ˙ 2 ) = 5 m l 2 6 θ ˙ 2 Write the expression for the potential energy ( V 1 ) : V 1 = 0 For position 2: Write the expression for the displacement ( h ) of bar AB : h = ( l 2 − l 2 cos θ ) = l 2 ( 1 − cos θ ) ( ∵ ( 1 − cos θ = 2 sin 2 θ 2 ) ) = l 2 2 sin 2 θ 2 For small oscillation 2 sin 2 θ 2 ≈ θ 2 2 . h = l 2 θ 2 2 = l 4 θ 2 Write the expression for the kinetic energy ( T 2 ) : T 2 = 0 Write the expression for the displacement ( h 1 ) of collar: h 1 = ( l − l cos θ ) = l ( 1 − cos θ ) ( ∵ ( 1 − cos θ = 2 sin 2 θ 2 ) ) = l ( 2 sin 2 θ 2 ) For small oscillation 2 sin 2 θ 2 ≈ θ 2 2

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

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Chapter 19.3, Problem 19.84P

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The period (τn) of vibration of the system.

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Chapter 19.3, Problem 19.83P

Chapter 19.3, Problem 19.85P

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3. The cold-drawn AISI 1040 steel bar shown in the figure is subjected to a completely reversed axial load fluctuating between 28 kN in compression to 28 kN in tension. Estimate the fatigue factor of safety based on achieving infinite life (using Goodman line) and the yielding factor of safety. If infinite life is not predicted, estimate the number of cycles to failure. 25 mm + 6-mm D. 10 mm

CORRECT AND DETAILED SOLUTION WITH FBD ONLY. I WILL UPVOTE 1. The truss shown is supported by hinge at A and cable at E.Given: H = 4m, S = 1.5 m, α = 75⁰, θ = 33⁰.Allowable tensile stress in cable = 64 MPa.Allowable compressive stress in all members = 120 MPaAllowable tensile stress in all members = 180 MPa1.Calculate the maximum permissible P, in kN, if the diameter of the cable is 20 mm.2.If P = 40 kN, calculate the required area (mm2) of member BC.3. If members have solid square section, with dimension 15 mm, calculate the maximum permissible P (kN) based on the allowable strength of member HI.ANSWERS: (1) 45.6 kN; (2) 83.71 mm2; (3) 171.76 kN

Chapter 19 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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The period ( τ n ) of vibration of the system.

Solution Summary: The author shows the position of displacement as in Figure (1).

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The period (τn) of vibration of the system.

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Chapter 19 Solutions