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Amplitude is a key concept in simple harmonic motion (SHM). It represents the maximum displacement of a particle from its equilibrium position. In this context, the amplitude is the farthest point the particle reaches during its motion on either side of the equilibrium position. The amplitude is measured in meters, symbolized as \( A \), and is always positive. Even if the particle moves left, right, up, or down, the amplitude remains the same:- Amplitude helps us identify the energy in the system. The larger the amplitude, the greater the energy the particle possesses.- For this exercise, the given amplitude \( A \) is \( 0.1 \) meters. This tells us the maximum displacement the particle achieves from the equilibrium position. Understanding amplitude provides insight into how far the particle travels and aids in calculating other properties of SHM, like the maximum velocity.

Angular frequency measures how quickly a particle oscillates in simple harmonic motion. It indicates how many oscillations occur in a unit of time and is denoted by the symbol \( \omega \). Angular frequency is measured in radians per second. In simple harmonic motion, the angular frequency is related to the acceleration and displacement using the equation \( a = -\omega^2 x \). By substituting the known values, you can solve for \( \omega \):- For this exercise, the displacement \( x \) is \( 0.02 \) meters and acceleration \( a \) is \( 0.5 \) \( \text{ms}^{-2} \). This gives \( \omega^2 = \frac{|a|}{x} \) leading to an angular frequency of \( 5 \) \( \text{s}^{-1} \).The angular frequency helps in calculating the maximum velocity, providing insight into how swiftly the oscillations occur.

In simple harmonic motion, maximum velocity occurs when the particle passes through the equilibrium position. At this point, the speed is at its highest because all the potential energy has been converted into kinetic energy.Maximum velocity \( v_{\text{max}} \) can be calculated using the formula \( v_{\text{max}} = A\omega \), where \( A \) is amplitude and \( \omega \) is angular frequency:- In this exercise, with an amplitude of \( 0.1 \) meters and an angular frequency of \( 5 \ \text{s}^{-1} \), substituting these values gives us \( v_{\text{max}} = 0.5 \ \text{ms}^{-1} \).Understanding maximum velocity is crucial for predicting how fast the particle will move at different points in its oscillation cycle. It describes the peak speed the particle can achieve, which is a critical characteristic of its motion.