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A mass-spring system has k = 56.8 N/m and m = 0.46 kg.

A) Find the frequency of its simple harmonic motion. Express your answer with the appropriate units.

B) Find the angular frequency of its simple harmonic motion. Express your answer with the appropriate units.

C) Find the period of its simple harmonic motion. Express your answer with the appropriate units.

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Respuesta :

Answer:

A. [tex]\omega=11.1121\ rad.s^{-1}[/tex]

B. [tex]f=1.7685\ Hz[/tex]

C. [tex]T=0.5654\ s[/tex]

Explanation:

Given:

  • spring constant, [tex]k=56.8\ N.m^{-1}[/tex]
  • mass attached, [tex]m=0.46\ kg[/tex]

A)

for a spring-mass system the frequency is given as:

[tex]\omega=\sqrt{\frac{k}{m} }[/tex]

[tex]\omega=\sqrt{\frac{56.8}{0.46}}[/tex]

[tex]\omega=11.1121\ rad.s^{-1}[/tex]

B)

frequency is given as:

[tex]f=\frac{\omega}{2\pi}[/tex]

[tex]f=\frac{11.1121}{2\pi}[/tex]

[tex]f=1.7685\ Hz[/tex]

C)

Time period of a simple harmonic motion is given as:

[tex]T=\frac{1}{f}[/tex]

[tex]T=0.5654\ s[/tex]

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