(a) Explanation Given Information: The weight ( W ) of the block A is 3 lb. The spring constant ( k ) is 2 lb/in . The upward velocity ( x ˙ ) of is 90 in ./s . The acceleration due to gravity value ( g ) is 32.2 m/s 2 . Calculation: Calculate the mass ( m ) using the relation: m = W g Substitute 3 lb for W and 9.81 m/s 2 for g . m = 3 32.2 = 0.09317 lb ⋅ s 2 / ft Calculate the natural circular frequency ( ω n ) using the relation: ω n = k m Substitute 2 lb/in . for k and 0.09317 lb ⋅ s 2 / ft for m . ω n = 2 lb/in . × ( 12 ft 1 in . ) 0.09317 = 16.05 rad/s Write the expression for displacement ( x ) using simple harmonic motion: x = x m sin ( ω n t + ϕ ) (1) Here, x m is amplitude, ω n is natural circular frequency, t is time, and ϕ is phase angle. When time ( t ) is 0 the position ( x ) of the block is 0. Calculate the angle ( ϕ ) : Substitute 0 for t and 0 for x 0 = x m sin ( ω n ( 0 ) + ϕ ) ϕ = 0 Differentiate the equation (1), x ˙ = x m ω n cos ( ω n t + ϕ ) (2) Substitute 0 for ϕ and 0 for t in equation (2). x ˙ = x m ω n cos ( ω n ( 0 ) + ( 0 ) ) x ˙ = x m ω n ( 1 ) x ˙ = x m ω n (3) Substitute 0 for ϕ in equation (2) (b) To determine The corresponding velocity ( v ) and acceleration ( a ) of the block.

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

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,

Videos

Question

Chapter 19.1, Problem 19.11P

(a)

To determine

The time (t) required for the block to move 3 in.(↑).

(b)

To determine

The corresponding velocity (v) and acceleration (a) of the block.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.1, Problem 19.10P

Chapter 19.1, Problem 19.12P

Students have asked these similar questions

work due to spring (N.m) angular velocity in position (2) (rad/s)

9. A Proell governor has three fly balls, each of mass 4 kg. The lengths of all the arms are 280 mm and distance of each pivot of arm from the axis of rotation is 35 mm. The length of extension of lower arms on which each fly ball is attached is 70 mm, and inclined at 25° to the lower arm. The mass of the sleeve is 50 kg. Knowing that the arms are inclined at 50° to the axis of rotation and frictional force between spindle and sleeve is 45 N, determine the maximum and minimum equilibrium speeds of the governor.

A 2000-kg truck is being used to lift a 400-kg boulder B that is on a 50-kg pallet A. Knowing the acceleration of the rear-wheel-drive truck is 1 1 m 10.6 m m/s?, determine (a) the reaction at each of the front wheels, (b) the force between the boulder and the pallet. 1.4 m > +2 m→ <1.2 m→ A

Chapter 19 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.2P 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 - Prob. 19.8P Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The time ( t ) required for the block to move 3 in . ( ↑ ) .

Solution Summary: The author explains the time ( t ) required for the block to move.