A 2.15 kg damped harmonic oscillator has an angular frequency of 0.261 rad/s.If the amplitude is 2.9 m at t = 0.0 s and the object is at its maximum displacement at this time, what is the object's displacement at t= 4.01 s if the damping constant is 0.74 kg/s.

The basic form of the differential equation of damped oscillation is:



The undamped frequency of osciallation (i.e. if c = 0) is:



The term
is the damping ratio for the system. If < 1 then the system is underdamped and oscillations gradually grow smaller over time. If > 1 then it's over-damped and no oscillations occur.

If < 1 then the damped oscillation frequency is given by



If you plug in the numbers you can find , and from that the displacement at t= 4.01s.