Solving Simple Harmonic Motion: Cart Position and Time Comparison

AI Thread Summary
The discussion revolves around solving a simple harmonic motion problem involving an air-track cart oscillating on a spring, with its position described by the equation x = (12.5 cm)cos[(18.0 s^-1)t]. The main question is to determine the time t when the cart first reaches a position of x = 12.2 cm. Participants clarify the meaning of the angular frequency (s^-1) and its relation to the period of oscillation, emphasizing that T is not the same as t. The conversation highlights the need for further assistance in isolating t in the equation. The thread seeks collaborative input to solve the problem effectively.
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Homework Statement


The position of a an air-track cart that is oscillating on a spring is given by (12.5cm)cos[(18.0s-1)t].
At what value t after t=0 is the cart first located at x=12.2 cm?

The Attempt at a Solution


12.2 cm = (12.5cm)cos[(18.0s^-1)t].

How do I factor t out?

Thanks
 
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What is s?
 
I believe s^-1 is f which is equivalent to 1/T. T is period which is not equal to t time. Anyone could help me?
 

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