Question

If two s.H.M.'s are represented by equations y1=10 sin[3pit+pi/4] and y2=5[sin (3pit)+31/2cos(3pit)],then find the ratio of their amplitudes & phase difference in b/w them.

Answer 1

Hey mate,

◆ Answer-
Ratio of amplitudes = 2
Phase difference = π/4 rad


◆ Explaination-
# Given-
Comparing both eqn with std form y = A.sin(wt+θ),
We can say that -
A1 = 10 units
θ1 = π/4 rad
A2 = 5 units
θ2 = 0 rad
w = 3π

# Calculations
Ratio of amplitudes-
A1/A2 = 10/5 = 2

Phase difference-
φ = θ1 - θ2 = π/4 rad

Hope this helps you...

Answer 2

Answer:

ratio of amplitude is equal to 1

phase difference is is π/12