Physics · Oscillations · NEET
It is pi/2 rad (90 degrees). Write x = A sin(wt). Then v = dx/dt = A w cos(wt) = A w sin(wt + pi/2). The +pi/2 inside the sine means velocity leads displacement by 90 degrees. In simple words, velocity reaches its peak a quarter cycle BEFORE displacement reaches its peak.
It is pi rad (180 degrees). With x = A sin(wt), acceleration a = -w^2 A sin(wt) = w^2 A sin(wt + pi). The +pi means acceleration is exactly opposite in phase to displacement. So when the particle is at the extreme (x = +A), acceleration is maximum but points back toward the mean position (negative). This is why a = -w^2 x always has a minus sign.
It is pi/2 rad (90 degrees). Velocity leads displacement by 90 degrees and acceleration leads displacement by 180 degrees, so acceleration leads velocity by 180 - 90 = 90 degrees. When speed is maximum (at the mean position) acceleration is zero, and when acceleration is maximum (at the extreme) velocity is zero. They are a quarter cycle apart.
Leading means earlier. Velocity leads displacement, so velocity reaches its maximum first, then a quarter of a time period later displacement reaches its maximum. A phase difference of 90 degrees equals a time gap of T/4, because 360 degrees corresponds to one full period T.
In SHM the restoring force always pulls the particle back to the mean position. When the particle moves right to +A, the force and hence acceleration point left toward the centre. So displacement and acceleration always have opposite signs, which is exactly a 180 degree (pi) phase difference. This is the meaning of the SHM condition a = -w^2 x.
The phase difference between displacement and acceleration of a particle in simple harmonic motion is
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Acceleration leads velocity, and velocity leads displacement. Going in the order displacement, velocity, acceleration, each next quantity leads the previous one by 90 degrees (pi/2).
A phase difference of pi/2 equals a time difference of T/4, where T is the time period. So velocity peaks one quarter of a cycle before displacement peaks.
At the mean position displacement is zero, velocity is maximum, and acceleration is zero. The 90 degree gaps explain this: when x is zero, v is at its peak, and a follows x so it is also zero there.
Remember the ladder 0, 90, 180 degrees. Displacement is the reference (0), velocity is +90, acceleration is +180. So x-v is 90, v-a is 90, and x-a is 180 degrees.
Yes. The phase differences between the three quantities do not depend on whether you write x as sine or cosine. Velocity is always 90 degrees ahead of displacement and acceleration is always 180 degrees away from displacement.
