My Learning Cart
?
Categories
Account

A mass-spring system oscillates with a natural frequency of 3 Hz. If a damping f

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: 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?

Options:

  1. 2.8 Hz
  2. 2.9 Hz
  3. 3.0 Hz
  4. 3.1 Hz

Correct Answer: 2.9 Hz

Solution: 

New frequency (ω_d) = ω_n√(1-ζ²) = 3√(1-0.1²) ≈ 2.9 Hz.

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?
  1. 2.8 Hz
  2. 2.9 Hz
  3. 3.0 Hz
  4. 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.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks