A mass-spring system is subjected to a periodic force. If the amplitude of the f

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Question: 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?

Options:

0.1 m/s
0.2 m/s
0.3 m/s
0.4 m/s

Correct Answer: 0.2 m/s

Solution:

Maximum velocity (v_max) = Aω, where ω = 2πf. Assuming f = 1 Hz, v_max = 0.1 * 2π * 1 = 0.2 m/s.

A mass-spring system is subjected to a periodic force. If the amplitude of the f

Practice Questions

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.
Step 7: Calculate v_max: v_max = 0.1 * 2π ≈ 0.2 m/s.

Forced Oscillation – The behavior of a mass-spring system when subjected to an external periodic force.
Damping – The effect of a damping coefficient on the amplitude and velocity of oscillations.
Maximum Velocity – The peak speed of the oscillation, calculated using amplitude and angular frequency.
Angular Frequency – The rate of oscillation, related to the frequency of the periodic force.

A mass-spring system is subjected to a periodic force. If the amplitude of the f

What’s inside this PDF?

A mass-spring system is subjected to a periodic force. If the amplitude of the f

Practice Questions

Questions & Step-by-Step Solutions

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