Answer:
0.38296 m
1.02132 rad
[tex]x(t)=0.38296cos(12.24744 t+1.02132)[/tex]
Explanation:
Angular frequency is given by
[tex]\omega=\sqrt{\dfrac{k}{m}}\\\Rightarrow \omega=\sqrt{\dfrac{300}{2}}\\\Rightarrow \omega=12.24744\ rad/s[/tex]
Displacement is given by
[tex]x(t)=Acos(\omega t+\psi)\\\Rightarrow 0.2=Acos(12.24744\times 0+\psi)\\\Rightarrow 0.2=Acos\psi\\\Rightarrow A=\dfrac{0.2}{cos\psi}[/tex]
Velocity is given by
[tex]v=-A\omega sin(\omega t+\psi)\\\Rightarrow -4=\dfrac{0.2}{cos\psi}12.24744sin(12.24744\times 0+\psi)\\\Rightarrow 4=\dfrac{1}{cos\psi}2.449488sin(\psi)\\\Rightarrow tan\psi=\dfrac{4}{2.449488}\\\Rightarrow \psi=tan^{-1}\dfrac{4}{2.449488}\\\Rightarrow \psi=1.02132\ rad[/tex]
The phase angle is 1.02132 rad
[tex]A=\dfrac{0.2}{cos\psi}\\\Rightarrow A=\dfrac{0.2}{cos1.02132}\\\Rightarrow A=0.38296\ m[/tex]
The amplitude is 0.38296 m
The equation is given by
[tex]x(t)=Acos(\omega t+\psi)\\\Rightarrow x(t)=0.38296cos(12.24744 t+1.02132)[/tex]
The equation is [tex]x(t)=0.38296cos(12.24744 t+1.02132)[/tex]
