Answer:
Explanation:
Given
Amplitude [tex]A=10 cm[/tex]
mass of body [tex]m=5 gm[/tex]
maximum velocity [tex]v_{max}=100 cm/s[/tex]
if [tex]x=A\cos (\omega t)[/tex] is the general equation of SHM
where [tex]\omega =natural\ frequency\ of\ oscillation[/tex]
[tex]A=maximum\ amplitude[/tex]
[tex]t=time[/tex]
maximum amplitude is [tex]v_{max}=A\omega [/tex]
[tex]100=10\times \omega [/tex]
[tex]\omega =10 cycle/s[/tex]
and velocity at any instant is given by
[tex]v=\omega \sqrt{A^2-y^2}[/tex]
[tex]50=10\sqrt{10^2-y^2}[/tex]
[tex]5=\sqrt{10^2-y^2}[/tex]
squaring
[tex]25=100-y^2[/tex]
[tex]y^2=75[/tex]
[tex]y=5\sqrt{3}\ cm[/tex]
