Physics · Oscillations · NEET
Average velocity = net displacement / time. Over one full period the particle comes back to the exact starting point, so net displacement = 0, giving average velocity = 0. Distance is the total path length, which keeps adding up as the particle moves back and forth. It never subtracts, so it is 4A, not zero. Two different questions: velocity cares about start-to-end, distance cares about the whole journey.
In one period the particle goes mean to +A, back to mean, to -A, back to mean. Each of these four legs has length A. So total path length = A + A + A + A = 4A. The amplitude A is the maximum distance from the mean position, so each leg is exactly one amplitude long.
Average speed = total distance / time = 4A / T. Since w = 2*pi/T, we get T = 2*pi/w, so average speed = 4A / (2*pi/w) = 2Aw/pi. This is NON-zero, unlike average velocity. Do not confuse average speed (4A/T) with maximum speed (Aw).
In half a period the particle goes from +A to -A (or extreme to extreme). Net displacement = 2A, time = T/2. So average velocity = 2A / (T/2) = 4A/T = 2Aw/pi. Notice this equals the average SPEED over a full period. Over a full period, though, average velocity is again zero.
No. Instantaneous velocity at the mean position is the maximum, equal to Aw. Average velocity over a full cycle is zero, and average speed over a full cycle is 2Aw/pi (about 0.637*Aw). These are three different numbers, so read the question carefully to see which one is asked.
The average velocity of a particle executing SHM over one complete vibration is
The distance covered by a particle undergoing SHM in one time period is (amplitude = A)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Zero, because the net displacement over one full period is zero (the particle returns to its starting point).
4A, where A is the amplitude. The particle covers four legs of length A each.
Average speed = 4A/T = 2Aw/pi (about 0.637 times the maximum speed Aw). It is non-zero.
No. Maximum speed is Aw (at the mean position). Average speed over a period is 2Aw/pi, which is smaller.
2A. The particle moves from one extreme to the other, covering two legs of length A.
