Theory of the Modes

(I don't usually bother apologizing for my bad writing and for my horrible use of grammar and punctuations. Generally it is because of my simple acknowledgement of the fact that I am horrible at grammar and punctuations. But, I am going to apologize for this particular piece as it is going to get posted without a second glance, due to a lack of time. The reason for my lack of time to review this write up will go down as my attempts to learn and understand better Modal theory and its applications in engineering. To all the unassuming souls who chance upon this piece, my sincerest apologies if this turns out to be a murder of the english language and writing.)

      Modal Analysis theory is the study of the dynamic responses of systems and one of its approaches is to break down the responses into summations of contributions of various modes. Essentially what it says is that "what happens to you or how your life pans out can be broken down into a sum of the contributions of the people/events that you cross paths with and how strongly it can impact the various inherent modes in you". The contribution no matter how large or small, how negative or positive has a part in the sum total. So if you are happy right now as you read this, then it is not wrong to assume that a large/tiny bit of that is because of me and my effort in writing this piece of nonsense.

     To try and make you understand better I am going to try and talk to you about the essentials of a dynamic response and try and compliment it with a day to day life experience. To begin with, it is essential to understand that to get a response from a system some force has to act on it. As mentioned before, the reaction to this force can be broken down as an combination of the different response modes of the system that this force manages to excite. Forces can be positive or negative and if the forces are instantaneous, then one of the characteristics it exhibits is that the responses to these tend to die with time. The amplitude of the response decreases as time passes by. 

     Imagine you are running late to a seminar. The mismanagement of time on your part is to be blamed on the guy in your lab, a bad listener, who kept you engaged even after you told him you had to rush. The negative impact brings a frown on your face as your plans get offset in time. As you inch closer to the seminar hall the intensity of the frown decreases. (Amplitude tends to die with time!). 

   Note also that the initial amplitude the excitation (being late) has produced will depend on how effectively it has excited the modes. If in this case, you were not looking forward to the seminar with as much enthusiasm as you would have to a Manchester United  Vs Real Madrid match up, then the irritated frown mode might not get excited well enough to be noticed. (The modes need not be well excited by a force)

    As the effects of being late started to die out, a smile appears on your face. You seem to have perfectly timed your entry into a lift to coincide with that of a girl you have been wanting to speak to but not managed to so far. The positive excitation increases in amplitude. The girl and you being the only people in the lift, she asks you for the time and you get to reply to her. Amplitude hits peak. Big wide smile as you exit the lift and you forget about why you are late. (The happy smile mode is excited very well by the external excitation.)

     A few seconds down the line you realize, that was a chance to introduce yourself and get her name too might be?.. The 'hmmm.. I am so dumb' mode gets well excited and you trudge with heavy steps into the seminar hall and take a seat to listen to the talk. If you are lucky enough, the talk might be one of the most brilliant technical seminars you have attended and might excite your 'Woah.. that's interesting..!' mode. Whether this new response mode can help mask the earlier response that highlights  your not so great social skills and ability to strike a conversation, will depend totally on the system and the level to which each mode has been activated.

    To summarize, most of the dynamic responses can be broken down as a sum of responses to a combination of harmonic excitations with contribution of the modes excited varying depending on the systems construction. It might be of interest to note that a system that undergoes persistent forces (positive or negative) tends to show different characteristics with time. This can attributed to changing modal or system characteristics upon submission to repeated and persistent forces. Keeping aside such situations, usually the modal analysis theory can be used to address any system issues or to understand better the system characteristics.

A Walk Down Mt.Olympus

(Over the years I have been very fascinated by various professionals in various fields for the challenges and adventures they faced in their field of work on a daily basis. When I was young enough for my actions to be acceptable, my fascination often culminated in me trying to live a make belief life in the shoes of these people. A bus conductor, a coconut tree climber, the guy who milks the cow, the barber etc, I am told, were my idols for the period of two months of summer vacation I spent every year at my grandmothers. Twenty years later, society would lock me up somewhere if I were to play make belief on such 'trivial' professions and contrastingly hold me in high esteem if I exhibit more sophisticated taste of profession such as engineering or medicine. Well, today I am going to relive the old days of role play and play the part of a sports journalist (nothing that warrants getting locked up somewhere), a role I have envied and admired for ages now. With an appeal to be excused issued addressed all the good sports writers out there and anybody who plays any kind of sport who might beg to differ with my views.. Here i go...)

The 'legends of a sport' are essentially those hands that rock the cradle that is their respective sports. Its they who inspire the moments of brilliants all across the sport. Whether it be with the very gifts that god has given them or with the will that they created in the countless others who work hard and play hard to try and one day become like their idols. Yet the credit and respect don't come so easy and it is usually never the rosy picture that hindsight provides in most of the stories of these legends. The Jordan's and the Schumacher's have all had their ups and downs. However, what sets them apart is probable their reactions to those situations.

Over last few months too many sporting Idols seem to be coming to the end of their lives of being invincible. We have Lance Armstrong shattering his 'idol'hood with a brave cry of acceptance of his mistakes, though only after being backed into a corner. Sachin Tendulkar is starting to feel that there is only so long that he can fight against the greatest opponent of them all - Time. Roger Federer seems to finally have gone from No:1 among the fab four to No:4.

As an ardent sports lover I have wondered for quite sometime as to how difficult the lives of these stars must be. How they manage to put up with the life where everyone seems to be eagerly waiting for them, more often than not, to come crashing down. There must be no worse feeling than to be dragged down from the top of the mountain that you once conquered. Quite often than not it can shatter ones resolve and will. Yet the fact that they manage to drive themselves to continue forward, try and climb to those heights again, love what they do and carry on is indeed an admirable quality.

Only sometime ago at the Australian Open, Andy Murray had Roger Federer's number and was all over him. The match was probably one of his most dominant displays over Federer. Yet Federer scratched and pulled and hung on and before anyone realised we were into a fifth set. The years when the Fedex dominated, questions were raised about his greatness because the general feeling was competition was poor. Then came along Rafael Nadal, a champion who sacrificed his body to be able to beat Federer and people questioned his greatness again. Now, here he stands, unable to overcome the combination of a champion opponent and an aging body and the world seems to saying that he will never be the same again because of the time that has passed by.

From being the sole person in charge of the fates of a team of 11, picked from a billion people, and having carried that responsibility with aplomb for more than a decade, Sachin Tendulkar has come to a state where he is being questioned by every Tom, Dick and Harry on the street. I am not suggesting here that his previous achievement or service entitles him to preferential treatment but just wondering at how he is still able to focus on his responsibilities when everyone seems to be doubting him. Might be the answer is as simple as his love for the sport but one cannot ignore the mental strength probably necessary to be able to block out everything else that gets thrown at him so that he can just play the sport that he likes.

Lance Armstrong seems to have disappointed the whole of the planet, but over the interviews he seems to be pleading for a second chance. Here is a man who has fought cancer and founded a noble institution to inspire other fights against cancer and people just want to see the man grounded to dust rather see him given a chance to make up for his mistakes. While this probably is not one battle which will happen in a sports arena, the little part of me that considered him a legend for so long wishes him all the very best in what is undoubtedly going to be the biggest battle of his life yet. I hope that he is given a chance to change and that we get to see a wonderful inspiring story from the man after all.

Ironically though, it is probably during this walk down the olympus they lived in so long that it becomes more clear than ever as to why they deserve their tags as champions and probably a small insight into how the mind of a champion works. While everyone sees a Federer trying to scrape past his younger, fitter peers in the top four and struggling, what Fedex himself sees is probably his biggest challenge yet - a fight against time. While people are calling for his head Sachin Tendulkar is probably thinking only about beating age and slowing reflexes one more time.

Sports fans have always loved a good comeback. We love a suspense thriller style script and what better than a falling star who rises up. I believe its this liking of the fans that continually push them to support the underdogs and write off champions. All in the little hope of getting to witness something special. Well, this is probably one situation where the fans can write off these champions and not be served a second half with a reaction that will give you goosebumps. This is after all a fight against time. It is precisely because of this that I feel that its time to not complain too much and instead sit back and enjoy their spirit and valor while its still on display. Try not to keep your hopes high and instead focus on the good things while they last. Because the familiarity of the script points towards this being a 'Braveheart' type movie where you are standing up and applauding, goosebumps and all, while the protagonist walks into the sunset, not having been able to accomplish the impossible but having left an lump in your heart with effort and passion he showed in his attempts.