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Two shm are given by Y1 =40sinwt and Y2=10(sinwt+c.coswt). If their displacement are equal , then the value of c is

Two shm are given by Y1 =40sinwt and Y2=10(sinwt+c.coswt). If their  displacement are equal , then the value of c is 

Grade:12

1 Answers

vikas askiitian expert
509 Points
11 years ago

Y2 = 10(sinwt + c.coswt)

 divide & multiply by (1+c2)1/2

 Y2 =10(1+c2)1/2 [ sinwt(1/1+c2)1/2 + (c2/1+c2)1/2coswt ]

now put (1/1+c2)1/2 = cos@ then

            (c2/1+c2)1/2 = sin@

now Y2 becomes

Y2 = 10(1+c2)1/2 [ sinwtcos@ + coswtsin@]

Y2 = 10(1+c2)1/2[sin(wt+@)]

Y1 = 40sinwt

for same displacement , amplitude must be same so

 40 = 10(1+c2)1/2

  c = 151/2

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