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JEE Main 2022 (29 Jun, Shift 1) · Velocity & Acceleration in SHM

Velocity & Acceleration in SHM question from JEE Main 2022 (29 Jun, Shift 1)

Q50JEE Main 2022 · 29 JUN · SHIFT 1Medium

Velocity & Acceleration in SHM

A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position. The new amplitude of vibration is $\sqrt{x}$ cm. The value of x is _____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 700

At $x = 5$ cm: $v = \omega\sqrt{10^2 - 5^2} = \omega\sqrt{75}$ .
Tripled speed $v' = 3\omega\sqrt{75}$ , same $\omega$ .
$A'^2 = x^2 + \frac{v'^2}{\omega^2} = 25 + 9\times 75 = 700$ .
$A' = \sqrt{700}$ cm, so $x = 700$ .

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