(a) Explanation Given information: The mass of the sphere B ( m ) is 2 kg . The length of the bar AB ( l ) is 400 mm or 0 .4m . The spring constant ( k ) is 3.5 kN/m . The magnitude of the vertical displacement ( δ ) is δ m sin ω f t . The displacement ( δ m ) is 3 mm or 0.003 m . The forced circular frequency ( ω f ) is 1 5rad/s . Calculation: Show the deflection diagram of the beam ABC as Figure (1). Take the moment about A ( M A ) as follows: ∑ M A = 0 m l θ ¨ = 1 2 ( k δ m sin ω f t − k l 2 θ ) m l 2 θ ¨ = 1 2 k δ m sin ω f t l − k l 2 4 θ m l 2 θ ¨ + k l 2 4 θ = k l δ m 2 sin ω f t θ ¨ + k l 2 4 m l 2 θ = k l δ m 2 m l 2 sin ω f t θ ¨ + k 4 m θ = k δ m 2 m l sin ω f t (1) The expression for the amplitude of motion ( θ ) as follows: θ = θ m sin ω f t (2) Compare the equation (1) and (2). θ m = k δ m 2 m l The expression for the general equation of the differential equation as follows: θ ¨ + ω n 2 θ = 0 (3) Compare the equation (1) and (3) (b) To determine Find the magnitude of the maximum acceleration of sphere B ( l ω f 2 θ m ) .

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 19.4, Problem 19.107P

(a)

To determine

Find the magnitude of the maximum angular velocity of bar AB (ωfθm).

(b)

To determine

Find the magnitude of the maximum acceleration of sphere B (lωf2θm).

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Chapter 19.4, Problem 19.106P

Chapter 19.4, Problem 19.108P

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Find the magnitude of the maximum angular velocity of bar AB ( ω f θ m ) .

Solution Summary: The author shows the deflection diagram of the beam ABC as Figure (1).