A forced oscillator has a mass of 3 kg and is driven by a force of 12 N at a frequency of 2 Hz. What is the amplitude of the oscillation if the damping coefficient is 0.1 kg/s?
Practice Questions
1 question
Q1
A forced oscillator has a mass of 3 kg and is driven by a force of 12 N at a frequency of 2 Hz. What is the amplitude of the oscillation if the damping coefficient is 0.1 kg/s?
0.1 m
0.2 m
0.3 m
0.4 m
Using F = mAω², we find A = F / (mω²) = 12 / (3*(2π*2)²) ≈ 0.2 m.
Questions & Step-by-step Solutions
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Q
Q: A forced oscillator has a mass of 3 kg and is driven by a force of 12 N at a frequency of 2 Hz. What is the amplitude of the oscillation if the damping coefficient is 0.1 kg/s?
Solution: Using F = mAω², we find A = F / (mω²) = 12 / (3*(2π*2)²) ≈ 0.2 m.
Steps: 8
Step 1: Identify the given values: mass (m) = 3 kg, force (F) = 12 N, frequency (f) = 2 Hz, damping coefficient (b) = 0.1 kg/s.
Step 2: Calculate the angular frequency (ω) using the formula ω = 2πf. Here, f = 2 Hz, so ω = 2 * π * 2.
Step 3: Calculate ω: ω = 4π ≈ 12.57 rad/s.
Step 4: Use the formula for amplitude (A) of the forced oscillator: A = F / (mω²).
Step 5: Calculate ω²: ω² = (4π)² = 16π².
Step 6: Substitute the values into the amplitude formula: A = 12 / (3 * 16π²).
Step 7: Calculate the denominator: 3 * 16π² ≈ 150.8.
Step 8: Finally, calculate A: A ≈ 12 / 150.8 ≈ 0.0796 m, which is approximately 0.08 m.
