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Speed suddenly tripled at a given displacement: find the new amplitude

The same question, asked 2 times: 29 Jun 2022*, 31 Jan 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    29 Jun 2022

    24
    A body is performing simple harmonic motion with an amplitude of 10 cm10\text{ }cm. The velocity of the body was tripled by air Jet when it is at 5 cm5\text{ }cm from its mean position. The new amplitude of vibration is x\sqrt{x} cmcm. The value of xx is

  2. Question 2

    31 Jan 2024

    29
    A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is 2 A3\frac{2\text{ }A}{3}. The new amplitude of motion is nA3\frac{nA}{3}. The value of nn is ______ .