A particle executes simple harmonic motion represented by the displacement function x(t)=A sin(ω t+φ). If the position and velocity of the particle at t=0 s are 2 cm and 2ω cm s⁻¹ respectively, then its amplitude is x√2 cm, where the value of x is .

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2. x(0)=A sin φ=2 cm and v(0)=Aω cos φ=2ω gives A cos φ=2 cm. Squaring and adding, A²=8, so A=2√2 cm and x=2.

A particle executes simple harmonic motion represented by the displacement function x(t)=A sin(ω t+φ). If the position and velocity of the particle at t=0 s are 2 cm and 2ω cm s⁻¹ respectively, then its amplitude is x√2 cm, where the value of x is ______.

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