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IIT JEE Class 11 2019 : Select

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	Mayank Kumar Singh Jamshedpur	+Fave Message
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Damped Harmonic Motion. A particle is said to be in harmonic motion if its displacement is proportional to the applied force (resultant force) and is directed opposite to it . Nature provides a large number of cases in which restoring forces acts which causes simple harmonic motion as this force only causes the displacement to be directed opposite to the force acting that time means it just helps to slow down the body and then again restoreback its original position. Now dampingforce from my view point is also a jealous friend of resultant force see as the restoring force acts oopposute he present displacement as in the case of the pendulum when it is going from mean position to the other side (extreme position) during this journey it just acts as damping force. DAMPING FORCE arise due to frictional surface wear and tear of parts.as damping force acts in opposite direction it causes loss of energy(total energy).a Damping force is proportional to speed as in case of friction we all know friction face is independent of the area of contact of body it depends on the normal and normal force is the force or reaction force and it can be increased only when external action force is more and the one way is to increase the momentum which is the simplest case as it would add to to the force applied.Now one would think unit of momentum and fice is different then how can they be same so theirs not much difference between them in their unit only a difference of t (not consider difference as minus) means if u divide momentum by time it becomes force means range of change of momentum is the force applied in some interval of time to make the force large we generally consider small time interval.so when we change the momentum of system it means we are just applying a force on it. So now we have understood damping is proportion to velociy or to be more specific negative of velocity. FORCED OSCILLATION AND RESONANCE The above case we studied previously was about Damped harmonic motion now there is another interesting case when a force as restoring force and the damping force all acts see here motion is complicated but after sometime the body again begins to oscillate periodically as in the beginning it takes time means there is some time lapse during which the force taks to counterbalance each other so during that period motion is complictaed and as the force encounters its countering force and reduce s to zero(means in most of the time its seen that only restoring force is left and damping force and the force acting counterbalance each other. IF we vary the no of cycles or no of turns of the applied force amplitude changes and becomes maximum when new angular frequency or no of cycles turn out to be = .so this condition when on varying the angular frequency ,amplitude becomes maximum called the case of resonance. Now coming to the point when angular frequency omega is not varied and we want resonance to To occur just in that case as no forced oscillation is their so in that case is the case of small damping it negligible damping and as angular frequency is same or unvaried so it must equal to the original natural frequency. Now we have just said that when damping is very small or present the angular frequency is equal to the natural frequency. Now we haven t talked what would happen when damping force is not present in case of forced vibration then amplitude becomes infinity as we have already said that as the damping force tends to 0 omega or angular frequency attains its natural value and Now I will discuss how amplitude becomes infinity as going by the equation of aplitude. Now we know to make amplitude infinity the tears at below should turn out to be zero so here is the gateway to get the logic see why I told that damping force. Should be zero ???this was because b would turn out to be zero and noe only left over term is Angular frequency. Which would. Turn to be zero as to small damping case we know omeganatural is equal to omega at any instant so Amplitude turns out to be infinity so keeping this in mind bridges are made so that this factor does causes or doesn t increased its amplitude turns it to be infinity.

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