Final answer:
To estimate the damping constant c and the spring constant k in a mass-spring-damper system, we can use the decay formula for amplitude and the formula for angular frequency. Plugging in the given information, we find that the damping constant is approximately 0.306 and the spring constant is approximately 94.68.
Step-by-step explanation:
To estimate the damping constant c and the spring constant k, we can use the formula for the decay of amplitude in a damped mass-spring system:
A_n = A_0 * e^(-c/2m * n)
where A_n is the amplitude at the nth cycle, A_0 is the amplitude at the first cycle, c is the damping constant, m is the mass, and n is the cycle number.
In this case, A_1 = A_0 and A_30 = 0.2 * A_0. Plugging these values into the formula and solving for c, we get:
c = -2m * ln(0.2) / 30 = -2 * 100 * ln(0.2) / 30 ≈ 0.306
To find the spring constant k, we can use the formula for the angular frequency of a damped mass-spring system:
w = sqrt(k/m - c^2 / 4m^2)
where w is the angular frequency. Plugging in the values and solving for k:
k = (w^2 + c^2 / 4m) * m = (0.306^2 + 0.306^2 / 4 * 100) * 100 ≈ 94.68
Therefore, the damping constant c is approximately 0.306 and the spring constant k is approximately 94.68.