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Energy dependent phase lags reveal crucial information about the causalrelation between various spectral components and about the nature of theaccretion geometry around the compact objects. The time-lag and the fractionalroot mean square (rms) spectra of GRS 1915+105 in its heartbeat oscillationclass/$\rho$ state show peculiar behaviour at the fundamental and harmonicfrequencies where the lags at the fundamental show a turn around at $\sim$ 10keV while the lags at the harmonic do not show any turn around at least till$\sim$ 20 keV. The magnitude of lags are of the order of few seconds and hencecannot be attributed to the light travel time effects or Comptonization delays.The continuum X-ray spectra can roughly be described by a disk blackbody and ahard X-ray power-law component and from phase resolved spectroscopy it has beenshown that the inner disk radius varies during the oscillation. Here, wepropose that there is a delayed response of the inner disk radius (DROID) tothe accretion rate such that $r_{in}(t)\propto \dot{m}^\beta (t-\tau_d)$. Thefluctuating accretion rate drives the oscillations of the inner radius after atime delay $\tau_d$ while the power-law component responds immediately. We showthat in such a scenario a pure sinusoidal oscillation of the accretion rate canexplain not only the shape and magnitude of energy dependent rms and time-lagspectra at the fundamental but also the next harmonic with just four freeparameters.

A model for the energy-dependent time-lag and rms of the heartbeat oscillations in GRS 1915+105