Answer:
T = 0.375 s, f = 2.66 Hz and ω = 16.71 rad/s
Explanation:
Given that,
The mass of a harmonic oscillator, m = 0.5 kg
The force constant of the spring, k = 140 N/m
The frequency of a harmonic oscillator is given by :
[tex]f=\dfrac{1}{2\pi }\sqrt{\dfrac{k}{m}}[/tex]
Substitute all the values,
[tex]f=\dfrac{1}{2\pi }\sqrt{\dfrac{140}{0.5}} \\\\f=2.66\ Hz[/tex]
Time period is given by :
[tex]T=\dfrac{1}{f}\\\\T=\dfrac{1}{2.66}\\\\T=0.375\ s[/tex]
The angular frequency is given by :
[tex]\omega=2\pi f\\\\\omega=2\pi \times 2.66\\\\\omega=16.71\ rad/s[/tex]
Hence, this is the required solution.
