Topic: Theory of Machines
The equation of motion of a spring-mass-damper system is given by x'' + 4x' + 16x = 12 sin(5t). What is the damping factor of the system?
- A. 1
- B. 0.5
- C. 0.25
- D. 0.75
Answer: B. 0.5
Explanation: The standard differential equation of motion is x'' + 2*zeta*omega_n*x' + omega_n^2*x = F(t). Comparing this with the given equation: omega_n^2 = 16, so omega_n = 4 rad/s. Also, 2*zeta*omega_n = 4. Substituting omega_n gives 2*zeta*(4) = 4, so 8*zeta = 4, which means zeta = 0.5.