Answer:
[tex]\frac{KE}{TE} = \frac{15}{16}[/tex]
b)
[tex]\frac{U}{TE} = \frac{1}{16}[/tex]
Explanation:
Let the amplitude of SHM is given as A
so the total energy of SHM is given as
[tex]E = \frac{1}{2}kA^2[/tex]
now we know that
a)
kinetic energy is given as
[tex]KE = \frac{1}{2}k(A^2 - x^2)[/tex]
here
[tex]x = \frac{A}{4}[/tex]
so now we have
[tex]KE = \frac{1}{2}k(A^2 - \frac{A^2}{16})[/tex]
[tex]KE = \frac{15}{32}kA^2[/tex]
now its fraction with respect to total energy is given as
[tex]\frac{KE}{TE} = \frac{15}{16}[/tex]
b)
Potential energy is given as
[tex]U = \frac{1}{2}kx^2[/tex]
so we have
[tex]U = \frac{1}{32}kA^2[/tex]
so fraction of energy is given as
[tex]\frac{U}{TE} = \frac{1}{16}[/tex]
