Question

A. 5 kg mass is attached to a spring with spring constant k=100 N/m, and moves along a horizontal surface which produces a resistive force R=−bv where b=8 N/m/s.

a. Calculate what the angular frequency ω would be if there were no resistive force/damping Is the damped angular frequency greater of less than this?

Answer 1

The angular frequency of the oscillating mass-spring system can be calculated using ω = √(k / m). The damped angular frequency is always less than the angular frequency when there is no resistive force or damping, so, we can the value 4.47 rad/s.

Step-by-step explanation:

The angular frequency (ω) of an oscillating mass-spring system can be calculated using the formula ω = √(k / m), where k is the spring constant and m is the mass. In this case, the spring constant is 100 N/m and the mass is 5 kg. Plugging in the values, we get ω = √(100 / 5) = √20 = 4.47 rad/s.

The damped angular frequency (ωd) is always less than the angular frequency when there is no resistive force or damping. This is because damping causes energy loss in the system, resulting in a decrease in frequency. Therefore, the damped angular frequency will be less than 4.47 rad/s in this case.