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aabhas upadhyay Grade: 12

a particle executin shm covers a distance x in first second from its mean position and it covers distance y in another one second. find amplitude of the particle

7 years ago

Answers : (1)

AJIT AskiitiansExpert-IITD
68 Points

Dear aabhas ,

the genreal equation of shm is     x(t) =  Asin(wt)

so just plug in the values given in the quesiton and solve ....x

x = A sinw ------(1)

y = Asin2w - Asinw

y =2Acosw *sinw - Asinw

y = (2cosW -1) *x

cosw =(y/x+1)/2 =  (x+y)/2x

so sinw  = (1-cos2w)1/2  = ( 1 -(x+y/2x)2)1/2  =  (3x2-y2-2xy)1/2 / 2x

putting in eqn 1

A = x/sinw  = 2x2/(3x2-y2-2xy)1/2   

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7 years ago
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