Final answer:
The period of the mass-spring system with a spring constant of 1.8 × 10^2 N/m and a 1.6 kg mass is approximately 0.56 seconds.
Step-by-step explanation:
Calculating the Period of a Mass-Spring System
The period of a mass-spring system can be found using the formula for the period T of a simple harmonic oscillator, which is T = 2π√(m/k), where m is the mass of the object attached to the spring and k is the spring constant. In this case, we have a mass m = 1.6 kg and a spring constant k = 1.8 × 102 N/m. Plugging these values into the formula, we get:
T = 2π√(1.6 kg / 1.8 × 102 N/m)
Which gives us:
T = 2π√(0.0088889 kg·m/N)
T = 2π√(0.0088889) s
T approximately equals 0.560 s
Therefore, the period of the mass-spring system is approximately 0.56 seconds.