Two simple harmonic motions are represented as y₁ = 10sin ω t and y₂ = 5sin ω t + 5cos ω t, both in cm. The ratio of the amplitudes of y₂ ( A₂) to that of y₁ ( A₁), is (a) 4: 1 (b) √(2): 1 (c) 1: 1 (d) 1: √(2)

Answer: (d). A₁ = 10 cm y₂ = 5sin ω t + 5cos ω t has A₂ = √(5² + 5²) = 5√(2) cm (A₂)/(A₁) = (5√(2))/(10) = 1/√(2) So the answer is (d) 1: √(2).

Two simple harmonic motions are represented as y₁ = 10sin ω t and y₂… | MHT CET 2026 (19 May, Shift 1)

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Periodic Motion & SHM Basics

Two simple harmonic motions are represented as $y_1 = 10\sin \omega t$ and $y_2 = 5\sin \omega t + 5\cos \omega t$ , both in cm. The ratio of the amplitudes of $y_2$ ( $A_2$ ) to that of $y_1$ ( $A_1$ ), is

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Answer: (d)

$A_1 = 10\text{ cm}$
$y_2 = 5\sin\omega t + 5\cos\omega t$ has $A_2 = \sqrt{5^2 + 5^2} = 5\sqrt{2}\text{ cm}$
$\frac{A_2}{A_1} = \frac{5\sqrt{2}}{10} = \frac{1}{\sqrt{2}}$
So the answer is (d) $1 : \sqrt{2}$ .

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Periodic Motion & SHM Basics question from MHT CET 2026 (19 May, Shift 1)

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