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

Question

G1 Physics · Accepted Answer

Initially: v = ω√(A² - x²) At x = 2A/3: v = (√5/3)Aω New speed: v' = 3v = √5 Aω If new amplitude is A': v'² = ω²[A'² - (2A/3)²] 5A² = A'² - 4A²/9 A'² = 49A²/9 A' = 7A/3 Therefore, n = 7