The graph shows how the displacement of a simple harmonic oscillator varies with time. Which of the following graphs shows how velocity varies with time for the same oscillator, ov... The graph shows how the displacement of a simple harmonic oscillator varies with time. Which of the following graphs shows how velocity varies with time for the same oscillator, over the same time period?
Understand the Problem
The question presents a displacement-time graph of a simple harmonic oscillator and asks to choose the correct corresponding velocity-time graph. Understanding the relationship between displacement and velocity in simple harmonic motion (SHM) is crucial.
Answer
Velocity is a quarter cycle out of phase with displacement in simple harmonic motion. This means that if displacement is a cosine function, velocity is a negative sine function.
The velocity in simple harmonic motion is a quarter cycle out of phase with the displacement. If displacement is a cosine function, velocity is a negative sine function.
Answer for screen readers
The velocity in simple harmonic motion is a quarter cycle out of phase with the displacement. If displacement is a cosine function, velocity is a negative sine function.
More Information
In simple harmonic motion (SHM), as displacement reaches its maximum, velocity is zero, and when displacement is zero, the velocity is at its maximum.
Tips
It's a common mistake to confuse the phase relationship between displacement and velocity in SHM. Remember that velocity leads displacement by 90 degrees or a quarter of a cycle.
Sources
- Mathematical Description of SHM - Digestible Notes - digestiblenotes.com
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