Answer:
Explanation:
Given
mass of block [tex]m=5.7\ kg[/tex]
at [tex]t=0 s[/tex]
displacement is [tex]x=-0.7\ m[/tex]
velocity [tex]v=-0.8\ m/s[/tex]
acceleration [tex]a=2.7\ m/s^2[/tex]
suppose [tex]x=A\cos (\omega t+\phi )[/tex] is the general equation of SHM
where A=amplitude
[tex]\omega [/tex]=natural frequency of oscillation
therefore velocity and acceleration is given by
[tex]v=-A\omega \sin (\omega t+\phi )[/tex]
[tex]a=A\omega ^2\cos (\omega t+\phi )[/tex]
for t=0
[tex]-0.7=A\cos (\phi )---1[/tex]
[tex]v=-0.8=-A\omega \sin(\phi)---2[/tex]
[tex]a=2.7=-A\omega ^2\cos(\phi )----3[/tex]
divide 1 and 3 we get
[tex]\omega ^2=\frac{27}{7}[/tex]
[tex]\omega =\sqrt{\frac{27}{7}}[/tex]
Now square and 1 and 2 we get
[tex](0.7)^2+(\frac{0.8}{\omega })^2=A^2[/tex]
[tex]A^2=0.49+0.166[/tex]
[tex]A=0.81\ m[/tex]
