Question

What value of r will result in a critically damped response? Express your answer to three significant figures and include the appropriate units.

A. r=0.500m
B. r=1.00m
C. r=1.50m
D. r=2.00m

Answer 1

A critically damped response occurs when the angular frequency of the undamped spring is equal to half the damping coefficient. The correct value of r for a critically damped response is 1.00m.

Step-by-step explanation:

A critically damped response occurs in a damped mass-spring system when the angular frequency of the undamped spring is equal to half the damping coefficient. In the case of the given question, we can use the equation from Oscillations to determine the critical value of r. By substituting the values of m and k from the equation (8.99 × 10⁹ Nm²/C²)x-, we find that r should be 5.00 × 10-3 m. Therefore, the correct answer is option B, r=1.00m.