Part A: The time period of the mass-spring system is 0.573 seconds.
Part B: The frequency of the vibration of the mass-spring system is 1.75 Hz.
Given that the mass of the spring is 1.5 kg and the spring constant is 1.8 × 10^2 n/m.
The period of the mass-spring system is given by the formula.
[tex]T=2\pi\sqrt{\dfrac {m}{k}}[/tex]
Where m is mass and k is spring constant.
Substituting the values in the above equation, we get the time period.
[tex]T = 2 \times 3.14 \times \sqrt{\dfrac {1.5}{ 1.8 \times 10^2}}[/tex]
[tex]T = 0.573 \;\rm s[/tex]
Hence the time period of the mass-spring system is 0.573 seconds.
The frequency of the vibration is given below.
[tex]f = \dfrac {1}{T}[/tex]
[tex]f = \dfrac {1}{0.573}[/tex]
[tex]f = 1.75 \;\rm Hz[/tex]
Hence the frequency of the vibration of the mass-spring system is 1.75 Hz.
To know more about the time period and frequency, follow the link given below.
https://brainly.com/question/13891370.
