  Information based uncertainty measures like R{\'e}nyi entropy (R), Shannon
entropy (S) and Onicescu energy (E) (in both position and momentum space) are
employed to understand the influence of radial confinement in isotropic
harmonic oscillator. The transformation of Hamiltonian in to a dimensionless
form gives an idea of the composite effect of oscillation frequency ($\omega$)
and confinement radius ($r_{c}$). For a given quantum state, accurate results
are provided by applying respective \emph{exact} analytical wave function in
$r$ space. The $p$-space wave functions are produced from Fourier transforms of
radial functions. Pilot calculations are done taking order of entropic moments
($\alpha, \beta$) as $(\frac{3}{5}, 3)$ in $r$ and $p$ spaces. A detailed,
systematic analysis is performed for confined harmonic oscillator (CHO) with
respect to state indices $n_{r},l$, and $r_c$. It has been found that, CHO acts
as a bridge between particle in a spherical box (PISB) and free isotropic
harmonic oscillator (IHO). At smaller $r_c$, $E_{\rvec}$ increases and
$R_{\rvec}^{\alpha}, S_{\rvec}$ decrease with rise of $n_{r}$. At moderate
$r_{c}$, there exists an interaction between two competing factors: (i) radial
confinement (localization) and (ii) accumulation of radial nodes with growth of
$n_{r}$ (delocalization). Most of these results are reported here for the first
time, revealing many new interesting features.
