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another 1...aieee-09
If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time ? (1) aT + 2
pv (2)aT/v2T2 + 4p2v2 (4)aT/x
(3) a
Comments (45)
there are 2 options correct...... even the a2 T2 + 4(pi)2 v2 is correct...
a=-ω2x
T=2(pi)/ω
....v=
so,a2T2 is ω4x2 4 (pi)2 ω-2 ..............and ........4(pi)2(ω2(A2 - x2))....so...if u sum them up and simplify,the term contaning x gets cancelled and u get,
........4(pi)2 ω2 A2 ..........WHICH IS CONSTANT!!!!!!.....
@lalit,karthik....
option c may not always be true
in the case of damped oscillation, A is an exponentially decaying function of time, isnt it?
whereas option d is true irrespective of the amplitude of oscillation, since it is the hallmark of any simple harmonic oscillation,
damped or otherwise, so it is the MOST appropriate, although people may argue that the question isnt specific......
people don't know how to question nowadyas.they willingly gave the answer an option as aT/x which most of us(even I) marked but they are canceling it on the basis that a/x isn't defined at x=0. but does the question asks about the domain or range of x. i mean agar defined nahi hai par jaaha pein define hai waha to constant hai.matlabF(X)={ x=9; x belongs to real-{1}} isn't constant......................argument on the basis of damping might not be justified as damping is not in syllabus...........they should have asked which one of the follwoing is always defined and constant.
well obviously one tends to assume that the question is related to wherever the function is defined and
3 may be rejected on the basis of damping........4 makes a lot more physical sense to me and i did think of situation at x=0 during the
exam but i like several others assumed the above.................vague question.......
it's a physics question. after all...
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