Answer :
Answer:
A = 6.9 cm
Explanation:
Simple Harmonic Motion
A mass-spring system is a common example of a simple harmonic motion device since it keeps oscillating when the spring is stretched back and forth.
If a mass m is attached to a spring of constant k and they are set to oscillate, the angular frequency of the motion is
[tex]\displaystyle w=\sqrt{\frac{k}{m}}[/tex]
The equation for the motion of the object is written as a sinusoid:
[tex]\displaystyle X=A\ cos\ w\ t[/tex]
Where A is the amplitude.
The instantaneous speed is computed as the derivative of the distance
[tex]\displaystyle X'=V=-A\ w\ sin\ w\ t[/tex]
And the maximum speed is
[tex]\displaystyle V_{max}= A\ w[/tex]
Solving for the amplitude
[tex]\displaystyle A= \frac{V_{max}}{w}[/tex]
Computing w
[tex]\displaystyle w =\sqrt{\frac{120}{0.2}}=24.5\ rad/ s[/tex]
Calculating A
[tex]\displaystyle A=\frac{1.7}{24.5}=0.069\ m[/tex]
[tex]\displaystyle \boxed{A=6.9\ cm}[/tex]