A mass-spring system oscillates with a natural frequency of 3 Hz. If a damping f
Practice Questions
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
Questions & Step-by-Step Solutions
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?
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.
Natural Frequency – The frequency at which a system oscillates when not subjected to any external force.
Damping Ratio – A dimensionless measure describing how oscillations in a system decay after a disturbance.
Damped Frequency – The frequency of oscillation of a damped system, which is lower than the natural frequency.
