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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
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
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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