We know that the velocity of a simple harmonic oscillator is given by,
Hence, comparing with (1) we have,
The period of the oscillations is given by,
The position of the particle is given by,
As seen in the figure, every 0.5 seconds the particle moves covers a distance of a, and hence in 2.5 seconds the particle will cover a distance of 5a. In the remaining 0.3 seconds, the particle will travel a distance of
(as in Problem 4.7).Hence the total distance traveled will be,
sir,
ReplyDeleteiam not satisfied with the solution to the question 4.9,i can never really grasp the meaning of the term probability,of finding a particle,please add some more physical explanation and picturisation of the problem
Sir has very well explained the mathematical esence of probability of finding a particle in particular position under simple harmonic Motion. Suppose you study the probability at a point P. Then the mass has higher probability of occurence or to be found at P and the differential region around P if its passes slowly through that region, then it spends more time in that region. Else wise it will have lower probability if passes through there in higher velocity and then will spend less time in that region.
DeleteThis is the physical logic behind the probability and its gradient
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