Select the correct answer.
When is the velocity of a mass on a spring at its maximum value?
A. when the mass has a displacement of zero
B. when the mass is moving downward
C. when the mass has maximum acceleration
D. when the mass is at rest
Answer (1)
The velocity of a mass on a spring is maximum at the equilibrium position.
The equilibrium position corresponds to zero displacement.
Maximum acceleration occurs at maximum displacement where velocity is zero.
Therefore, the velocity is at its maximum when the mass has a displacement of zero, so the answer is A .
Explanation
Problem Analysis We are asked to determine when the velocity of a mass on a spring is at its maximum value. Let's analyze each option.
Analyzing Option A Option A states that the velocity is at its maximum when the mass has a displacement of zero. This corresponds to the equilibrium position of the spring. At the equilibrium position, the restoring force is zero, and the mass has its maximum velocity as it passes through this point.
Analyzing Option B Option B states that the velocity is at its maximum when the mass is moving downward. While the mass is moving, its velocity is not necessarily at its maximum. The direction of motion does not guarantee maximum velocity.
Analyzing Option C Option C states that the velocity is at its maximum when the mass has maximum acceleration. Maximum acceleration occurs at the points of maximum displacement, where the restoring force is greatest. At these points, the velocity is zero, not maximum.
Analyzing Option D Option D states that the velocity is at its maximum when the mass is at rest. The mass is at rest at the points of maximum displacement, where the velocity is zero.
Conclusion Therefore, the velocity of a mass on a spring is at its maximum value when the mass has a displacement of zero.
Examples
Understanding the motion of a mass on a spring is crucial in many real-world applications. For example, the suspension system in a car uses springs and dampers to provide a smooth ride. The point where the spring is at equilibrium (zero displacement) is where the velocity of the oscillating mass is at its maximum, influencing the overall comfort and stability of the vehicle. Similarly, in musical instruments like tuning forks, the maximum velocity at the equilibrium point determines the loudness and clarity of the sound produced.
