Question

When the displacement of a mass on a spring is 0.515 of the amplitude of its oscillation, what fraction of the mass’s energy is kinetic energy?

thanks

Answer 1

x =A•sin( ω•t)

0.515 = A•sin( ω•t)
sin( ω•t) = 0.515.
sin² ( ω•t) = 0.27.
cos ²( ω•t) =1 - sin² ( ω•t) =1-0.27 =0.73.
KE =E(total) • cos ²( ω•t).
KE/ E(total) = cos ²( ω•t) = 0.73.