For Simple Harmonic Motion (SHM), the relationship between amplitude and period is not directly proportional. Instead, the period of SHM is independent of the amplitude of motion.
To understand this relationship, let's define amplitude and period in the context of SHM:
Amplitude: The amplitude (A) of a system undergoing SHM is the maximum displacement from the equilibrium position. It represents the furthest distance the object or particle moves from its equilibrium position during one complete cycle of motion.
Period: The period (T) of SHM is the time taken for one complete cycle of motion. It is the time it takes for the system to go through one full oscillation, starting from its initial position, going to the maximum displacement in one direction, returning to the equilibrium position, and then reaching the maximum displacement in the opposite direction before coming back to the equilibrium position again.
Mathematically, the relation between amplitude (A) and period (T) for SHM can be expressed as:
T = 2π * √(m/k)
where: T is the period of SHM. m is the mass of the object or particle undergoing SHM. k is the spring constant (also known as the force constant) of the system.
From this equation, you can see that the period (T) depends only on the mass (m) and the spring constant (k) of the system. It is independent of the amplitude (A) of the motion. Therefore, the amplitude of SHM does not affect the time taken for one complete cycle, which is the period of the motion.
In summary, in simple harmonic motion (SHM), the period (T) is determined by the mass and spring constant of the system and remains constant regardless of the amplitude (A) of the motion.