A particle performs simple harmonic motion with amplitude A . Its speed is increased to three times at an instant when its displacement is 2 A 3 . The new amplitude of motion is n A 3 . The value of n

Question

A particle performs simple harmonic motion with amplitude A . Its speed is increased to three times at an instant when its displacement is 2 A 3 . The new amplitude of motion is n A 3 . The value of n is _____.

TestHub · Accepted Answer

Speed in SHM in terms of displacement is given by, $v = ω \sqrt{A^{2} - x^{2}}$ .

at $x = \frac{2 A}{3}$ , we get

$v = ω \sqrt{A^{2} - {(\frac{2 A}{3})}^{2}} = \frac{\sqrt{5} A ω}{3}$

Let the new amplitude be $= A'$

Then,

$v' = 3 v \Rightarrow ω \sqrt{{(A')}^{2} - {(\frac{2 A}{3})}^{2}} = \sqrt{5} A ω$

$\Rightarrow A' = \frac{7}{3} A$

Therefore, $n = 7$ .

Physics - SHM Question with Solution | TestHub

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