Harmonic oscillator is significantly important in quantum gravity for its dynamical properties. Dynamics of the harmonic oscillator can be modified by inserting a modified uncertainty relation considered in quantum cosmology models such as string theory and quantum loop gravity theory. In this paper, the equation of damped quantum harmonic oscillator has been solved with respect to the modified uncertainty relation and the effects of this modification have been probed in the case of the damped oscillating system.
Here a theoretically relation is presented between the frequency and the temperature of a linear harmonic oscillator. A mathematical derivation is proved here, that shows how frequency of linear harmonic oscillator varies with the temperature. This is also shown that, at given frequency of oscillator only a minimum value of temperature can be found out till at particular limit. This theory also gives a new concept of quantization of temperature for harmonic oscillator or all the bodies whose are constructed of such type of oscillator. Term of uncertainty in temperature is also explained in this theory.