  Information-based uncertainty measures like Shannon entropy, Onicescu energy
and Fisher information (in position and momentum space) are employed to
understand the effect of \emph{symmetric and asymmetric} confinement in a
quantum harmonic oscillator. Also, the transformation of Hamiltonian into a
dimensionless form gives an idea of the composite effect of force constant and
confinement length ($x_c$). In symmetric case, a wide range of $x_{c}$ has been
taken up, whereas asymmetric confinement is dealt by shifting the minimum of
potential from origin keeping box length and boundary fixed. Eigenvalues and
eigenvectors for these systems are obtained quite accurately via an imaginary
time propagation scheme. For asymmetric confinement, a variation-induced exact
diagonalization procedure is also introduced, which produces very high-quality
results. One finds that, in symmetric confinement, after a certain
characteristic $x_{c}$, all these properties converge to respective values of
free harmonic oscillator. In asymmetric situation, excited-state energies
always pass through a maximum. For this potential, the classical turning-point
decreases, whereas well depth increases with the strength of asymmetry. Study
of these uncertainty measures reveals that, localization increases with an
increase of asymmetric parameter.
