If a damped oscillator has a mass of 5 kg, a spring constant of 20 N/m, and a da
Practice Questions
Q1
If a damped oscillator has a mass of 5 kg, a spring constant of 20 N/m, and a damping coefficient of 1 kg/s, what is the natural frequency of the system?
1 Hz
2 Hz
3 Hz
4 Hz
Questions & Step-by-Step Solutions
If a damped oscillator has a mass of 5 kg, a spring constant of 20 N/m, and a damping coefficient of 1 kg/s, what is the natural frequency of the system?
Step 1: Identify the values given in the problem. We have a mass (m) of 5 kg and a spring constant (k) of 20 N/m.
Step 2: Write down the formula for natural frequency (ω_n) of a damped oscillator, which is ω_n = √(k/m).
Step 3: Substitute the values into the formula. Replace k with 20 and m with 5: ω_n = √(20/5).
Step 4: Calculate the value inside the square root. 20 divided by 5 equals 4: ω_n = √4.
Step 5: Find the square root of 4, which is 2. Therefore, the natural frequency (ω_n) is 2 Hz.
Natural Frequency – The natural frequency of a damped oscillator is determined by the mass and spring constant, independent of the damping coefficient.
Damped Oscillator – A damped oscillator experiences a reduction in amplitude over time due to a damping force, but the natural frequency is calculated without considering damping.
