Practice question

**Sinusoidal description** links amplitude A and angular frequency ω to instantaneous values. Given x(t) = A cos(ωt), max acceleration ω²A quantifies force requirement F_max = m ω²A, and velocity at arbitrary x is v = ±ω√(A² - x²) from energy conservation. Displacement ( x = A cos (ω t + Φ) ) and velocity ( v = -ω A sin (ω t + Φ) ) differ by π/2 radians because the cosine and sine functions are shifted by this phase, reflecting their derivative relationship. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² =