A particle undergoes simple harmonic motion of amplitude x0 and frequency f . What is theaverage speed of the particle during one oscillation?

The average speed of a particle undergoing simple harmonic motion can be calculated using the formula for the total distance travelled divided by the total time taken.

Step 1: Determine the total distance travelled In one complete oscillation, the particle moves from one extreme to the center, then to the other extreme, and back to the center. This is equivalent to twice the amplitude (2x0) for each half oscillation, and since there are two half oscillations in one complete oscillation, the total distance is 4x0.

Step 2: Determine the total time taken The total time taken for one complete oscillation is the period of the motion, which is the reciprocal of the frequency, or 1/f.

Step 3: Calculate the average speed The average speed is the total distance travelled divided by the total time taken, or (4x0) / (1/f). Simplifying this gives 4x0f.

So, the average speed of the particle during one oscillation is 4x0f.