Air-Track Cart Oscillating on a Spring, solve for time

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SUMMARY

The position of an air-track cart oscillating on a spring is described by the equation (14.0 cm)cos[(12.0 s-1)t]. To determine when the cart first reaches a position of x=2.0 cm, the equation 2 = 14cos(12t) must be solved. The correct approach involves using the inverse cosine function, leading to the equation 12t = cos-1(1/7). The calculated time t = cos-1(1/7) / 12 yields an incorrect result of 6.816 seconds, indicating a need for further clarification on the calculation process.

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Homework Statement
The position of a an air-track cart that is oscillating on a spring is given by (14.0cm)cos[(12.0s-1)t]. At what value t after t=0 is the cart first located at x=2.0 cm?


The attempt at a solution

y = Acos(wt+∅)

y = 14cos(12t)
2 = 14cos(12t)
(1/7) = cos(12t)
12t = cos^-1(1/7)
t = cos^/1(1/7) / 12
t = 6.816 seconds,
incorrect.

Does anyone have any advice on how to proceed with this question?
 
Physics news on Phys.org
When finding the angle, be sure to express it in radians. cos^-1(1/7) = ??
 
Doc Al said:
When finding the angle, be sure to express it in radians. cos^-1(1/7) = ??

Thank you!
 

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