(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 ) .

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

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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).