What is the phase constant in SHM?

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The phase constant \(\phi\) in simple harmonic motion (SHM) is determined from the equation \(x(t) = A \cos(wt + \phi)\), where \(A\) is the amplitude and \(w\) is the angular frequency. To find \(\phi\), one can use the initial condition \(x(0) = A \cos(\phi)\), leading to the formula \(\phi = \cos^{-1}(x(0)/A)\). Alternatively, if the position \(x(t)\) is known at a specific time \(t\), \(\phi\) can be calculated using \(\phi = \cos^{-1}(x(t)/A) - wt\). The discussion highlights that for a specific scenario, this calculation results in a phase constant of \(0.5\pi\). Understanding the phase constant is crucial for analyzing oscillatory motion in SHM.
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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?
 

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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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