What is the phase constant in SHM?

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Homework Help Overview

The discussion revolves around determining the phase constant (\phi) in the context of simple harmonic motion (SHM), specifically using the equation x(t) = A cos(wt + \phi). Participants are examining the relationship between position, amplitude, and the phase constant based on a provided graph.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss methods to calculate the phase constant, including evaluating the position at specific times and using the inverse cosine function. There are questions about the implications of the measurements M, N, and T mentioned in the original post.

Discussion Status

The conversation includes attempts to clarify how to derive the phase constant from the given information. Some participants have provided formulas for calculating \phi, while others are seeking further assistance or validation of their approaches. There is no explicit consensus on the value of \phi yet.

Contextual Notes

There is mention of an attachment that requires approval, which may contain relevant visual information for the discussion. Additionally, the original poster references specific measurements (M, N, T) that are not fully explained in the thread.

polymerase
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The graph shows the position x of an oscillating object as a function of time t. The equation of the graph is x(t)=Acos(wt + \phi)
where A is the amplitude, w is the angular frequency, and \phi is a phase constant. The quantities M,N, and T are measurements to be used in your answers.

See attached image.

What is \phi in the equation?
 

Attachments

  • MHM_xt.jpg
    MHM_xt.jpg
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can anyone help me?
 
The attachment has to be approved, but the phase angle (constant) is found for example when t = 0, and knowing x(t=0) = A cos \phi, or

\phi = cos-1 (x(0)/A), or

if x(t) is known at t, then

\phi = cos-1 (x(t)/A) - wt
 
the answer leads to 0.5pi.
 

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