Question

Discuss analytically, the composition of two S.H.M.s of same period and parallel to each other. Find the resultant amplitude when phase difference is (i) 0 (ii) π (iii) π/2 (iv) π/3 radians.

Answer 1

I) 2A

II) 0

III) √2A

IV) A

Let the first SHM be y1 = Asin(wt) .

The second SHM will be -

y2 = Asin(wt+θ) as the two SHM will have the same amplitude and time period

θ is the phase difference between the first and the second SHM.

The resultant of the two SHM -

Y = y1 + y2

=> Y = Asin(wt) + Asin(wt + θ)

For θ = 0

Y = Asin(wt) + Asin(wt)

=> Y = 2Asin(wt)

The amplitude of the resultant SHM = 2A

For θ = π

Y = Asin(wt) + Asin(wt+ π)

=> Y = Asin(wt) - Asin(wt)

=> Y = 0

The amplitude of the resultant SHM = 0

For θ = π/2

Y = Asin(wt) + Asin(wt+ π/2)

=> Y = √2A sin(wt)

The amplitude of the resultant SHM = √2A

For θ = π/3

Y = Asin(wt) + Asin(wt+ π/3)

The amplitude of the resultant SHM = A

Answer 2

Answer:

Discuss analytically, the composition of two S.H.M.s of same period and parallel to each other. Find the resultant amplitude when phase difference is (i) 0 (ii) π (iii) π/2 (iv) π/3 radians.