When a body moves with simple harmonic motion, then the phase difference between the velocity and the acceleration is

In Simple Harmonic Motion (SHM), the displacement is typically represented as a sinusoidal function, such as x(t) = A sin(ωt). The velocity (v) is the first derivative of displacement, v(t) = Aω cos(ωt), which can be rewritten as Aω sin(ωt + π/2) [t1, t4]. This indicates that velocity leads displacement by a phase of 90° (π/2 radians) [t8]. The acceleration (a) is the derivative of velocity, a(t) = -Aω² sin(ωt), which is equivalent to Aω² sin(ωt + π) or Aω² cos(ωt + π/2) [t1, t7]. Consequently, the phase difference between velocity and acceleration is 90° (π/2 radians), with acceleration leading velocity [t1, t3]. While displacement and acceleration are 180° out of phase (opposite in sign), the relationship between the successive derivatives—displacement to velocity and velocity to acceleration—always involves a 90° phase shift [t4, t7].