Here's why:
* Period (T): The time it takes for one complete cycle of oscillation. The period is determined by the system's natural frequency, which is dependent on the mass and spring constant (or other restoring force) and not the amplitude.
* Frequency (f): The number of cycles per second. Since frequency is the inverse of the period (f = 1/T), it also remains constant.
* Amplitude (A): The maximum displacement from the equilibrium position. Doubling the amplitude increases the total distance traveled during one cycle.
* Velocity (v): The maximum velocity of the system increases proportionally to the amplitude.
* Acceleration (a): The maximum acceleration of the system increases proportionally to the amplitude.
In essence, doubling the amplitude increases the energy of the system, but it doesn't change how fast the oscillations happen (period).
