1. (I) If a particle undergoes SHM with amplitude 0.18 m, what is the total distance it travels in one period?

The total distance the particle travels in one period is approximately 1.131 m

Explanation:

The Simple Harmonic Motion (SHM) of an object can be conceptualized as the uniform circular motion of the object projected on an axis

Therefore, the amplitude of a SHM which is the largest displacement of the motion from its central or equilibrium position is equivalent to the radius of the circular motion

Therefore;

The amplitude of the SHM, a = 0.18 m = The radius of the equivalent circular motion, r

A period of SHM = The time it takes takes to complete one revolution

Therefore, the total distance traveled in one period = The length of 1 complete revolution = The circumference of the equivalent circle describing the SHM

The circumference of the equivalent circle describing the SHM, C = 2·π·r

By substituting the known value for the radius, 'r', we have;

C = 2·π·r = 2 × π × 0.18 m ≈ 1.131 m

Therefore, the total distance the particle travels in one period ≈ 1.131 m

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