The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m , 2 ms − 1 and 16 ms − 2 at a certain instant. The amplitude of the motion is

Question

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m , 2 ms − 1 and 16 ms − 2 at a certain instant. The amplitude of the motion is x ​ , m where x is ________

TestHub · Accepted Answer

​ x = 4 m , V = 2 m / s , a = 16 m / s 2 ∣ a ∣ = ω 2 x ⇒ 16 = ω 2 ( 4 ) ω = 2 rad / s v = ω A 2 − x 2 ​ A = ω 2 v 2 ​ + x 2 ​ ⇒ A = 4 4 ​ + 16 ​ A = 17 ​ m ​

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