A mass-spring system oscillates with a natural frequency of 3 Hz. If a damping force is applied, what is the new frequency of oscillation if the damping ratio is 0.1?
Practice Questions
1 question
Q1
A mass-spring system oscillates with a natural frequency of 3 Hz. If a damping force is applied, what is the new frequency of oscillation if the damping ratio is 0.1?
2.8 Hz
2.9 Hz
3.0 Hz
3.1 Hz
New frequency (ω_d) = ω_n√(1-ζ²) = 3√(1-0.1²) ≈ 2.9 Hz.
Questions & Step-by-step Solutions
1 item
Q
Q: A mass-spring system oscillates with a natural frequency of 3 Hz. If a damping force is applied, what is the new frequency of oscillation if the damping ratio is 0.1?
Solution: New frequency (ω_d) = ω_n√(1-ζ²) = 3√(1-0.1²) ≈ 2.9 Hz.
Steps: 8
Step 1: Identify the natural frequency (ω_n) of the system, which is given as 3 Hz.
Step 2: Identify the damping ratio (ζ), which is given as 0.1.
Step 3: Use the formula for the damped frequency (ω_d): ω_d = ω_n * √(1 - ζ²).
Step 4: Calculate ζ²: 0.1² = 0.01.
Step 5: Calculate (1 - ζ²): 1 - 0.01 = 0.99.
Step 6: Take the square root of 0.99: √(0.99) ≈ 0.995.
Step 7: Multiply the natural frequency by the square root: ω_d = 3 * 0.995 ≈ 2.985 Hz.
Step 8: Round the result to one decimal place: ω_d ≈ 2.9 Hz.
