Your teacher is correct. In the context of simple harmonic motion (SHM), the amplitude of the system is independent of the frequency. Let's break down the two scenarios you mentioned:
Resonance: In resonance, when an external force or frequency matches the natural frequency of a system, the amplitude of the system reaches its maximum value. This is because the system is driven at its natural frequency, and energy is efficiently transferred to it, resulting in large amplitude oscillations. In this case, the amplitude is indeed dependent on the frequency of the driving force or the external frequency applied to the system.
Simple Harmonic Motion (SHM): In the case of an undriven simple harmonic oscillator, where the system oscillates with a natural frequency determined by its own properties (e.g., mass and spring constant), the amplitude of the system is independent of the frequency. The amplitude is solely determined by the initial conditions of the system, such as the initial displacement and velocity. In SHM, the system oscillates with a constant amplitude regardless of the frequency of the oscillations.
Therefore, when studying simple harmonic motion, the amplitude of the system remains constant and is not affected by changes in frequency. However, during resonance, the amplitude can be influenced by the frequency of the external force.