Final answer:
The expression for the equivalent damping coefficient in a damped mass-spring system is β = b/2sqrt(mk).
Step-by-step explanation:
The expression for the equivalent damping coefficient in a damped mass-spring system can be obtained using the equation of motion for the system. The equation of motion for a damped mass-spring system is given by:
d²x/dt² + (b/m)dx/dt + (k/m)x = 0
where x is the displacement of the mass, t is time, b is the damping coefficient, m is the mass, and k is the spring constant.
The equivalent damping coefficient, denoted as β, is given by:
β = b/2sqrt(mk)
where β represents the ratio of the damping coefficient to the critical damping coefficient.