The time period of a periodic motion is the time it takes for one complete cycle or oscillation. It is typically denoted by the symbol T.
The relationship between time period (T) and amplitude (A) depends on the specific type of motion or wave being considered. However, assuming we are referring to simple harmonic motion (SHM), such as the motion of a pendulum or a mass-spring system, we can observe the following relationship:
T = 2π * √(m/k)
Where:
- T is the time period
- π is a mathematical constant (approximately 3.14159)
- m is the mass involved in the motion
- k is the spring constant (stiffness) of the system
In simple harmonic motion, the displacement is directly proportional to the amplitude. Therefore, if the displacement becomes half of its amplitude, we can say that the new displacement (D) is equal to half the original amplitude (A).
D = A/2
To determine the effect on the time period, we need to consider the relationship between displacement and time period in SHM. The time period is independent of the amplitude and depends only on the mass and stiffness of the system, as shown in the formula above. Thus, changing the displacement or amplitude does not directly affect the time period in simple harmonic motion. The time period remains the same unless there are changes in the mass or stiffness of the system.