Is it possible to transform a damping sine wave signal in time domain to frequency domain by using fft?

Hi all; I have a 1001 discrete data vector, which it gives a damped sine wave. I need to transform time-domain data to frequency domain data by using fft. when I used fft function, I get the plot as posted but I am not sure is it correct or not. Kindly, can any one assess fft result. Thanks in advance