Two simple harmonic motions are represented by the equations y1 = 10 sin

Text Solution

Solution : As `y_(2) = 5[sin(3pit)+sqrt(3)cos(3pit)]`……(1) <br> So if `5 = A cosphi` and `5sqrt(3) = A sinphi` <br> Then `A = sqrt(5^(2) + (5sqrt(3))^(2)) = 10` and `tanphi = (5sqrt(3))/(5) = sqrt(3)` so `phi = (pi)/(3)` <br> The above equation `(i)` becomes <br> `y_(2) = Acosphi sin(3pit) + Asinphi cos(3pit)` <br> `rArr y_(2) = Asin(3pit + phi) = 10 sin[3pit + ((pi)/(3))]` so, `(A_(1))/(A_(2)) = (10)/(10)` <br> `rArr A_(1) : A_(2) = 1 : 1`, Phase difference `= (pi)/(4) - (pi)/(3) = -(pi)/(12)`

Two simple harmonic motion, are represented by the equations y1=10 sin 3π t+π3 y2=5 sin 3π t+√3cos3π t Ratio of amplitude ofy1 to y2=x:1.The value of x is .

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App