(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, 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 m ω n ( 1 ) = x m ω n (3) Substitute 0 for ϕ in equation (2). x ˙ = x m ω n cos ( ω n t + 0 ) = x m ω n cos ω n t (4) Calculate the amplitude ( x m ) : Substitute 90 in ./s for x ˙ and 16.05 rad/s for ω n in equation (3). 90 in

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

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 19.1, Problem 19.12P

(a)

To determine

The position (x), velocity (v) and acceleration (a) of the block 0.90 sec after it has been struck by the hammer.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.1, Problem 19.11P

Chapter 19.1, Problem 19.13P

Students have asked these similar questions

الثانية Babakt Momentum equation for Boundary Layer S SS -Txfriction dray Momentum equation for Boundary Layer What laws are important for resolving issues 2 How to draw. 3 What's Point about this.

R αι g The system given on the left, consists of three pulleys and the depicted vertical ropes. Given: ri J₁, m1 R = 2r; απ r2, J2, m₂ m1; m2; M3 J1 J2 J3 J3, m3 a) Determine the radii 2 and 3.

B: Solid rotating shaft used in the boat with high speed shown in Figure. The amount of power transmitted at the greatest torque is 224 kW with 130 r.p.m. Used DE-Goodman theory to determine the shaft diameter. Take the shaft material is annealed AISI 1030, the endurance limit of 18.86 kpsi and a factor of safety 1. Which criterion is more conservative? Note: all dimensions in mm. 1 AA Motor 300 Thrust Bearing Sprocket 100 9750 เอ

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

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 position ( x ) , velocity ( v ) and acceleration ( a ) of the block 0.90 sec after it has been struck by the hammer.

Solution Summary: The author calculates the mass (m) using the relation: m=Wg Substitute 3 lb for W and 9.81

Concept explainers

Videos

The position (x), velocity (v) and acceleration (a) of the block 0.90 sec after it has been struck by the hammer.

Want to see the full answer?

Chapter 19 Solutions