In the study of oscillations, understanding the relationship between amplitude and various parameters is crucial. When the amplitude of an oscillation increases, it does not affect the period of oscillation. The period, denoted as \( T \), is related to the angular frequency \( \omega \) by the equation:

\( T = \frac{2\pi}{\omega} \)

Here, \( \omega \) is determined by the properties of the system, such as the spring constant \( k \) and mass \( m \), and is independent of amplitude. Therefore, an increase in amplitude does not lead to an increase in the period of oscillation.

Conversely, the maximum acceleration \( a_{\text{max}} \) is directly influenced by amplitude. The formula for maximum acceleration is given by:

\( a_{\text{max}} = \frac{k}{m} \cdot A \)

where \( A \) is the amplitude. As amplitude increases, \( a_{\text{max}} \) also increases, confirming that this statement is correct.

Next, the maximum speed \( v_{\text{max}} \) is also affected by amplitude, expressed as:

\( v_{\text{max}} = A \cdot \omega \)

Since \( \omega \) remains constant with changes in amplitude, an increase in amplitude directly results in an increase in \( v_{\text{max}} \).

When considering maximum kinetic energy \( K_{\text{max}} \), it is defined as:

\( K_{\text{max}} = \frac{1}{2} v_{\text{max}}^2 \)

Since \( v_{\text{max}} \) increases with amplitude, \( K_{\text{max}} \) also increases as a result.

The maximum potential energy \( U_{\text{max}} \) in a spring system is given by:

\( U_{\text{max}} = \frac{1}{2} k A^2 \)

As amplitude increases, \( U_{\text{max}} \) increases as well, indicating a direct relationship.

Finally, the total mechanical energy \( E_{\text{max}} \) of the system, which is the sum of kinetic and potential energy, is expressed as:

\( E_{\text{max}} = \frac{1}{2} k A^2 \)

Thus, an increase in amplitude leads to an increase in total mechanical energy, confirming that all aspects of energy in the system are positively correlated with amplitude.