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In the case of the forced vibration of a system, …

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Problem 140 Easy Difficulty

In Prob. $19.139,$ determine the required value of the coefficient of damping if the amplitude of the steady-state vibration of the element is to be 0.05 in.

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Vector Mechanics for Engineers: Statics and Dynamics

Chapter 19

Mechanical Vibrations

Section 5

Damped Vibrations

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everybody. So any here we have determined acquired value of the cowfish India peanut. The aptitude of the study state vibration element is 0.15 inches. So we have k equals tu que the spring when he goes to times £200 inches which goes 400 pounds inches. And we want those into pounds fee to get pounds one inch times one feet 12 inches. And this is going to give us £4800 per feet. So now we have our mass egos wait times gravity. And as for the £800 divided by 32.2 feet per second squared. So we get to 24.844 £7. Sundance beats about my feet. Okay? And we now we have we go and see here. Religious indicate about it. Buy em. So we got 4800 and we have your pound for feet divided by your 24 point eat four or seven pounds. Second wheat for a rooted which goes ups 13.90 radiance per seconds. Okay. And now we have a critical damping, which is to m omega en, which is gonna be two times 24 point E four for 77 pounds squared about of my feets divided by 13.90 radiance for seconds. And we're gonna get 6 £91 2nd heat And I always write my pounds away because it kind of looks like a wide So sometimes I'll get confused. Just a little tick there. Um, ex MP's now we gotta find X m. You're finding actually, the critical. So finding the sea here. Um, but we're using Excel formula for this. So we have this one minus. We could see. Okay, Yeah. Best squared. Plus two. We're trying to find the sea here. This critical. Okay. And that's where Rick is entirely claim beautiful and x m hear me. 0.15 inches. Okay. Equals £30. Divided by £400 divided by inches. Okay. And one minus 15.78 Divided by 13.90 A map and used units because the unit cancel out anyway. So I'm just not going right thumb. Did they cancel out? And now we have to use your see every 6 91 And this is anyone you can write units, so pound as beads Okay, 15.708 13.90. And I'm not gonna write these units because they cancel out. Okay, All square rooted. Okay? It's not gonna do seven 15 inches. There we go. Sometimes you just write it out. Um, the wrong number and you don't realize it until you're too late. So that 30 divided by 400 for me. 0 75 Okay. And it's gonna be inches and is Vita by 0.767 plus 1.698 times turned negative. Five c squared. Describe. And what we're gonna do is get this seed by it. So So we're gonna have 0.15 divide by 0.7 five. And actually, what would you do this if I could write? Yeah. You once again for the stylist tend to get back on here. Come on. There we go. 15 divided by 0.75 again. Remember that the injuries are gonna cancel out. And so we have that invited by and we have this one over. Was there close all X. Okay. So when we do that, I want to bring this up so you. 0.767 plus 1.69 eight times 10 to negative five times C squared and war doing is moving this over here. And when we do that, we have to flip it. 0.75 divided by 0.15 And this is gonna be squared, Dr. And now we're gonna get C squared. Equals we have this minus 0.75 0.15 squared minus 0.7 seven Oh, divided by 1.698 times 10 to negative five. OK, And so now we have the square roots of 0.1733 about it by 1.0 six 98 times 10 to negative. Five cry, Andi. Now we complain that ajar calculator, and you should get 127.3 pounds as to the feet. And if you need this and inches, it's gonna be 10.608 hounds, see and to inches okay. And us because we're using that pound INGE's times one feet. So instead of that is gonna be It's an inch times well, inches divided by feats. Right? So, in reality, what you're getting is I can write it a little better. You're doing 12 inches divided by and so you're dividing this whole thing by 12 basically. And you should get this. Okay, guys.

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Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek

Vector Mechanics for Engineers: Statics and Dynamics

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In the case of the forced vibration of a system, …

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Vector Mechanics for Engineers: Statics and Dynamics

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Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek

Vector Mechanics for Engineers: Statics and Dynamics

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Vector Mechanics for Engineers: Statics and Dynamics

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek Vector Mechanics for Engineers: Statics and Dynamics

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek

Vector Mechanics for Engineers: Statics and Dynamics