A hanging spring is compressed 3 inches from its rest position and released at t = 0 seconds. It returns to the same position after 0.8 seconds.
Find:
a) the amplitude of the motion
b) the period of the motion
c) the frequency of the motion
To find the answers to the given questions, we first need to understand the basic properties of harmonic motion.
Harmonic motion is characterized by three main properties: amplitude (A), period (T), and frequency (f).
Amplitude (A) represents the maximum displacement of the object from its equilibrium position. It is measured in the same units as the displacement, in this case, inches.
Period (T) is the time taken by the object to complete one full oscillation or cycle. It is measured in seconds.
Frequency (f) is the number of oscillations or cycles completed per unit time. It is measured in Hertz (Hz), which represents the number of cycles per second.
Now, let's go step by step to find the answers to the given questions:
a) To find the amplitude of the motion:
The amplitude of the motion is the maximum displacement from the rest position. In this case, the spring is compressed 3 inches from its rest position and returns to the same position, indicating that the amplitude is the distance the spring was compressed, which is 3 inches.
Therefore, the amplitude (A) of the motion is 3 inches.
b) To find the period of the motion:
The period of the motion represents the time taken for one complete oscillation. In this case, the spring returns to the same position after 0.8 seconds.
Therefore, the period (T) of the motion is 0.8 seconds.
c) To find the frequency of the motion:
The frequency of the motion represents the number of oscillations completed in one second. It is the reciprocal of the period.
Frequency (f) = 1 / Period (T)
Substituting the given value:
Frequency (f) = 1 / 0.8 seconds
Frequency (f) = 1.25 Hz
Therefore, the frequency (f) of the motion is 1.25 Hz.