1heyy u mean the correct option is (B).......................is der ne general method to approach to such ques somethin like by dimensional check or somethin like tht
if X,V and A denote displacement ,velocity and the accerleration of a particle executing SHM of time period T ,then which of the follownig will not change with time???
1.A2T2 + 4k2V2
2.AT/X
3.AT+2kX
4.AT/V note,
k=pie
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9 Answers
1The correct answer is (B)
x=A\sin (\omega t+\phi ) ;V=A\omega \cos (\omega t +\phi ) ;a=-A\omega ^{2}\sin (\omega t+\phi )
aT=-A\omega ^{2}T\sin (\omega t+\phi )=-A\omega ^{2}\times \frac{2\Pi }{\omega }\sin (\omega t+\phi )
=-2\Pi A\omega \sin (\omega t+\phi )
\frac{aT}{x}=-2\Pi \omega =Constant.
1
39Dimensional checks wouldn't help in checking the constancy of some value wrt another value..best way is to differentiate. Here lubu has taken the standard eqn for displacement in SHM and differentiated it to check.
1gr8 answer. Lubu edit ur post u posted that option (c) is correct instead of (b) and it's actually (b))according to ur soln.
1if you take the standered equation , then option 1 is also coming to be constant,
lube as per your equation
T2A2w4sin2(wt) + 4k2A2w2cos2(wt)
4k2 = T2w2
so
T2A2w4sin2(wt) + T2A2w4cos2(wt)
T2A2w4=constant
note k=pie and w=omega
i have considered the phase difference to be zero
isn't this correct, if its wrong the please point out the mistake
1hey guys can you find out the mistake in what i have done , unable to undersatnd where i am going wrong
1arey bhai how did u take accleration as constant ???
since u got T2A2ω4
in this u cannot consider accleration A as constant as it varies according to sine function....as in general equation... a = -ω2Asin(ωt + φ)
that's where u made a mistake ....[1]
1btw manmay , A is not accerleration, its the amplitude of the sine function ,now thats a constant???
1and wat is mentioned in the question look carefully......
it is mentioned that X - amplitude not A.........
lubu used usual symbols to avoid confusion ..........but u shuld remember the question has different notations for usual notations as mentioned in books