Question

If two SHM’s are represented by equations

y₁ = 10 sin [3πt +(π/4)] and, y₂ = 5 [ sin (3πt) + √3 cos (3πt)] the ratio of their amplitudes is

• A. 2 : 1
• B. 1 : 2
• C. 1 : 1
• D. 1 : $\sqrt{2}$

Answer 1

Answer: (C)

1 : 1

Answer 2

y₂ = 5 [sin (3πt) + $\sqrt{3}$ cos (3πt) ]

= 5 × 2 [$\frac{1}{2}$ sin (3πt) + $\frac{\sqrt{3}}{2}$ cos (3π t)]

= 10 [sin (3π t + $\frac{\pi}{3}$)]

A₂ = 10 and A₁ = 10

A₁/A₂ = 1 ⇒ A₁ : A₂ = 1 : 1