Answer
(a) $3.2Hz$
(b) $7.1cm$
(c) $5J$
Work Step by Step
(a) We can find the required frequency as
$f=\frac{1}{2\pi}\sqrt{\frac{K}{m}}$
We plug in the known values to obtain:
$f=\frac{1}{2\pi}\sqrt{\frac{2000}{5}}$
$\implies f=3.2Hz$
(b) We know that
$v=\omega \sqrt{A^2-x^2}$
We plug in the known values to obtain:
$1=(20)\sqrt{A^2-(0.5)^2}$
This simplifies to:
$A=7.1cm$
(c) We know that
$T.E=\frac{1}{2}KA^2$
We plug in the known values to obtain:
$T.E=\frac{1}{2}(2000)(7.1)^2$
$\implies T.E=5J$
