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JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Elasticity & SHM

Two simple harmonic motion, are represented by the equations

y_{1} = 10 sin (3 π t + \frac{π}{3})

y_{2} = 5 (sin 3 π t + 3 cos 3 π t)

Ratio of amplitude of

y_{1}

to

y_{2} = x : 1

. The value of

x

is ____

Answer: 1

Solution

Amplitude of

y_{1}

is

A_{1} = 10

. For

y_{2}

, rewrite as

y_{2} = 5 sin 3 π t + 53 cos 3 π t

. The amplitude is

A_{2} = 5^{2} + (53)^{2} = 25 + 75 = 100 = 10

. The ratio

\frac{A _{1}}{A _{2}} = \frac{10}{10} = 1

, so

x = 1

.

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Integer answer

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