An apparatus for diagnosing crack of a battery pack, the apparatus comprising: a sensing unit configured to generate a first time-vibration signal indicating time-dependent changes in vibration of the battery pack for a first measurement period, a second time-vibration signal indicating time-dependent changes in vibration of the battery pack for a second measurement period after the first measurement period and a third time-vibration signal indicating time-dependent changes in vibration of the battery pack for a third measurement period after the second measurement period; and a processor operably coupled to the sensing unit, wherein the processor is configured to: generate first spectral density data based on the first time-vibration signal, generate second spectral density data based on the second time-vibration signal, generate third spectral density data based on the third time-vibration signal, detect a first plurality of peaks from the first spectral density data, detect a second plurality of peaks from the second spectral density data, detect a third plurality of peaks from the third spectral density data, calculate a first rate of frequency change at a frequency of a first peak based on a difference between the frequency of the first peak and a frequency of a second peak, wherein the first peak is one of the first plurality of peaks and the second peak is one of the second plurality of peaks; determine the first peak as being a first characteristic peak when the first rate of frequency change is within a predetermined first reference range, calculate a second rate of frequency change at a frequency of a third peak based on a difference between the frequency of the first characteristic peak and the frequency of the third peak, wherein the third peak is one of the third plurality of peaks, determine that the battery pack is cracked when the second rate of frequency change is outside of a predetermined second reference range, and determine that the battery pack is uncracked when the second rate of frequency change is within the predetermined second reference range. a sensing unit configured to generate a first time-vibration signal indicating time-dependent changes in vibration of the battery pack for a first measurement period, a second time-vibration signal indicating time-dependent changes in vibration of the battery pack for a second measurement period after the first measurement period and a third time-vibration signal indicating time-dependent changes in vibration of the battery pack for a third measurement period after the second measurement period; and a processor operably coupled to the sensing unit, wherein the processor is configured to: generate first spectral density data based on the first time-vibration signal, generate second spectral density data based on the second time-vibration signal, generate third spectral density data based on the third time-vibration signal, detect a first plurality of peaks from the first spectral density data, detect a second plurality of peaks from the second spectral density data, detect a third plurality of peaks from the third spectral density data, calculate a first rate of frequency change at a frequency of a first peak based on a difference between the frequency of the first peak and a frequency of a second peak, wherein the first peak is one of the first plurality of peaks and the second peak is one of the second plurality of peaks; determine the first peak as being a first characteristic peak when the first rate of frequency change is within a predetermined first reference range, calculate a second rate of frequency change at a frequency of a third peak based on a difference between the frequency of the first characteristic peak and the frequency of the third peak, wherein the third peak is one of the third plurality of peaks, determine that the battery pack is cracked when the second rate of frequency change is outside of a predetermined second reference range, and determine that the battery pack is uncracked when the second rate of frequency change is within the predetermined second reference range. generate first spectral density data based on the first time-vibration signal, generate second spectral density data based on the second time-vibration signal, generate third spectral density data based on the third time-vibration signal, detect a first plurality of peaks from the first spectral density data, detect a second plurality of peaks from the second spectral density data, detect a third plurality of peaks from the third spectral density data, calculate a first rate of frequency change at a frequency of a first peak based on a difference between the frequency of the first peak and a frequency of a second peak, wherein the first peak is one of the first plurality of peaks and the second peak is one of the second plurality of peaks; determine the first peak as being a first characteristic peak when the first rate of frequency change is within a predetermined first reference range, calculate a second rate of frequency change at a frequency of a third peak based on a difference between the frequency of the first characteristic peak and the frequency of the third peak, wherein the third peak is one of the third plurality of peaks, determine that the battery pack is cracked when the second rate of frequency change is outside of a predetermined second reference range, and determine that the battery pack is uncracked when the second rate of frequency change is within the predetermined second reference range.