A mass-spring system is subjected to a periodic force. If the amplitude of the f
Practice Questions
Q1
A mass-spring system is subjected to a periodic force. If the amplitude of the forced oscillation is 0.1 m and the damping coefficient is 0.2 kg/s, what is the maximum velocity of the oscillation?
0.1 m/s
0.2 m/s
0.3 m/s
0.4 m/s
Questions & Step-by-Step Solutions
A mass-spring system is subjected to a periodic force. If the amplitude of the forced oscillation is 0.1 m and the damping coefficient is 0.2 kg/s, what is the maximum velocity of the oscillation?
Step 1: Identify the given values. The amplitude (A) is 0.1 m and the damping coefficient is 0.2 kg/s.
Step 2: Understand the formula for maximum velocity (v_max) in a mass-spring system under forced oscillation, which is v_max = Aω.
Step 3: Recognize that ω (angular frequency) can be calculated using the formula ω = 2πf, where f is the frequency.
Step 4: Assume a frequency (f) of 1 Hz for this calculation.
Step 5: Calculate ω using the assumed frequency: ω = 2π * 1 = 2π.
Step 6: Substitute the values into the maximum velocity formula: v_max = 0.1 * 2π.
