New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here


by: Chloe Reilly
Chloe Reilly

GPA 3.62

Aldo Ferri

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Aldo Ferri
Class Notes
25 ?




Popular in Course

Popular in Mechanical Engineering

This 0 page Class Notes was uploaded by Chloe Reilly on Monday November 2, 2015. The Class Notes belongs to ME 6442 at Georgia Institute of Technology - Main Campus taught by Aldo Ferri in Fall. Since its upload, it has received 10 views. For similar materials see /class/234240/me-6442-georgia-institute-of-technology-main-campus in Mechanical Engineering at Georgia Institute of Technology - Main Campus.

Similar to ME 6442 at

Popular in Mechanical Engineering


Reviews for Vibration


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 11/02/15
ME6442 Dr Ferri Example Problem 27 In this example a block of mass ml is dropped onto a springmassdamper platform having mass m2 stiffness k and Viscous damping constant C The platform is originally in static equilibrium with the weight of m2 alone Mass ml strikes platform m2 with an initial speed of V1 and does not rebound The displacement xt is referenced to the position of the unstretched spring positive down ml 4 kg m2 08 kg k 600 Nm X C 20 N sm g 9807 msAZ zeta C2sqrtkmlm2 damping ratio 0 damped natural frequency rads n sqrtkmlm2 natural frequency rads wd wntsqrtl zetaA2 This yields zeta 01863 wn 111803 and wd 109845 Now establish initial velocityjust before v1 and just after V2 impact Vl 5 ms hO VlA22g height from which ml was dropped V2 Vltmlmlm2 This yields h0 12746 and V2 41667 ms The initial conditions for the motion a er impact are x0 m2tgk initial disp m positive down V0 V2 positive down This yields x0 00131 and V0 41667 Finally the response can be calculated as follows x0 gwnA2 C V0 zetatwntclwd t 00000l2 x gwnA2exp zetawntclcoswdtt02sinwdt xdotl zetawnexp zetawntcltcoswdtt02sinwdt xdotl exp zetawnt wdtclsinwdtt02wdtcoswdt g xtwnAZ 2zetawnxdot The constants are determined to be c1 00654 and c2 03669 note typo in text The acceleration response is shown in Figure 1 for initial speeds of V1 5 ms and V1 2 ms Also shown is the acceleration of gravity g 9807 msz Liftoff occurs whenever xddot gt g It can be shown numerically that this occurs when V1 is greater than 25 ms approximately The displacements and velocity of the combined m1m2 system are shown in Figures 2 and 3 Note that for V1 5 the response beyond t 02769 seconds is not correct unless the block adheres to the platform a er impact Also note that the initial displacement is the same for both initial speeds Since x0 is constant but V0 differs by a factor of 25 the responses do not dilTer by a simple factor of 25 acceleration msz t 02769 sec 0 02 04 06 08 1 12 14 time sec Figure 1 Acceleration Response V15ms displacement m time sec Figure 2 Displacement Response oo Example 44 Dr Ferri o0 o0 EOM o0 o0 rhoALMprimexddot EALKprimex0 o0 o0 o0 Define lambda omegaA2rhoLA2E o0 o0 The theory says that as N gt infinity the scaled natural freqs should approach multiples of pi o0 o0 N50 d main2ones1N dsub ones1N 1L Kdiagd main diagd sub1 diagd sub 1 K1137 KNN3 7 7 Kprime NK MeyeN MprimeMN philameigKprimeMprime wnsqrtdiaglam N10 gives Wn39 31287 61803 90798 117557 141421 161803 178201 190211 197538 200000 oo wnlsortsortwn Re arrange the columns of phi consistent with the sorting used for w o0 o0 phi philsort muimat phi39Mprimephi 6 for N 10 off diag terms of muimat are order 35e 016 mu diagmu7mat PHlzerosNN 6 Normalize modes for j1N PHIiljphi1jSqrtmuj end for N 10 off diag terms of PHI39MPHI are order 35e 016 Note The normalized modes could also be normalized as PHlii PHIisqrtrhoAL figurel plotlNPHIl39o 391NPHI239A 39 xlabel39DOF 39 ylabel39Modes l and 2W legend39Mode 13939Mode 23939Location3939SouthEast39 if N gtlO figure2 plotlNPHI939o 391NPHI1039A W axis0 N 2 2 xlabel39DOF 39 ylabel39Modes 9 and 10W legend39Mode 93939Mode lO3939Location3939SouthEastW figure3 plotlNwn39o 391NlNpi39r 39 xlabel39Mode 39 ylabel39Nat Freq scaled39 legend39Lumped Mass Approximation3939Exact3939Location3939NorthWest39 err lOOabswn39 lNpi1Npi figure4 plotlNerr39rA W xlabel39Mode 39 ylabel39Percent Error in Nat Freq39 grid Modes I and 2 Modes 9 and IO DOF


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Anthony Lee UC Santa Barbara

"I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.