A linera hramonic oscillator of force costant $2\times {10}^{6}N/m$ and amplitude $0.01m$ has a total mechanical energy $160J$. Among the following statements, which are correct?

1	Maximum $PE$ is $100J$
2	Maximum $KE$ is $100J$
3	Maximum $KE$ is $160$
4	Manimum $KE$ is Zero

The correct option is C Both $\left(ii\right)$ and $\left(iii\right)$
Given,
Total mechanical energy,
$E_T=160J$
Force constant,
$k=2\times {10}^{6}N/m$
Amplitude,
$A=0.001m$
Maximum potential energy,
$\Rightarrow U_{max}=160J$
At extreme position, $KE$ is zero.So, the work done by sprimg force from exreme position to mean position is,
$\Rightarrow =\frac{}{2}k{A}^2$
Maximum Kinetic energy of body,
$k_{max}=\frac{1}{2}(2\times {10}^6)\left({0.01}^2\right)k_{max}=(1\times {10}^6)(1\times {10}^{-4})k_{max}=100J$
Maximum $PE$ is $160J$ and maximum is $KE$ is $100J$
And minimum potential energy,
$U_{min}=160-100=60J$