Concept of Resonance(as understood by me,correct me if I am wrong anywhere) Imagine a spring-mass system in which the mass is oscillating on the spring. Now imagine a variable force(the force varying sinusoidally) acting on the mass.If the maximum energy transfer has to take place,the force at anytime should not oppose the motion of the mass so that it does not decrease its kinetic energy.So when the mass is approaching the extreme position,the force should be acting towards the extreme position,as the mass retreats from the extreme position,the force should change direction and act towards the centre.The change in direction means that the force should become 0 at some time.If the force changes direction before the tension in the spring reverses,the force will oppose the masss motion as it reaches the extreme position.So we rule this out.If the force changes direction after the tension in the spring reverses,then at some time,the tension at some point will be more than the opposing force which is approaching 0 and cause the mass to move in a direction opposite to the force.Once again,the force will oppose the motion of the mass.So the force should become 0 at the same point at which the tension in the string becomes 0,then the force will not oppose the masss motion.As a result,the frequency of the sinusoidal force should match the natural frequency of the spring-mass system.That is resonance! As the the force is 0 at the extreme position at the extremes and its frequency=natural frequency,it should be 0 at the equilibrium position.If the force is ,for example,provided by another oscillating object,the force is proportional to its acceleration which is maximum at the driver objects maximum displacement position and the spring mass systems equilibrium position,therefore the driver objects oscillations are π/2 radians out of phase from the resonating system. This way,the applied force adds energy to the spring mass system,increasing its amplitude.Please correct me if I am wrong :)
Posted on: Sat, 15 Mar 2014 13:48:21 +0000
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