What Is the Maximum Speed of the Oscillator?

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The discussion revolves around determining the maximum speed of a mechanical oscillator given specific displacement and speed values. The user is confused about how to approach the problem and lacks clear examples or formulas in their textbook. They suggest that the oscillator is executing simple harmonic motion and reference the equation for displacement in terms of sine and cosine functions. However, they express uncertainty about how to derive parameters like omega, time, amplitude, or phase constant from the provided information. The conversation highlights a need for clearer guidance on solving such problems in physics.
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Homework Statement



A 253 g oscillator has a speed of 89.28 cm/s when the displacement is 2.79 cm and a speed of 70.95 cm/s when the displacement is 6.56 cm. What is the oscillator's maximum speed?


Homework Equations





The Attempt at a Solution



well, I haven't really attempted a solution because I'm totally confused on where to start with this problem. I've read the entire chapter and can't come up with any similar examples or formulas that would help solve this because it just doesn't give me enough information.

please help!
 
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Presumably this is a mechanical oscillator executing simple harmonic motion?

If that is the case, assume the displacement looks like
x(t) = A*cos(omega*t) + B*sin(omega*t)
and see what you can do to fit the given information.
 


Sorry I'm still very confused,
how can we find omega or t or A or B from any of the given information?

my book just doesn't explain at all how to handle this type of problem

and also that's the first time I've seen an equation written that way

I have seen the x(t) = Acos(w*t) and the one with the phase constant phi
 
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