Finding the expression of length of a spring given the relationship of speed and time

GeekOfMath

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May 9, 2017
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Hello!
I have been given a question that goes accordingly:
The speed at the end of a vibrating spring is given by the relationship v = 0.6 Cos 3t m/s. At time t=1, the spring has a length of 80cm. Find an expression for the length and hence its maximum length.
I'm at a loss. I don't know where to begin and what mathematics to apply. Please if you know anything that could help it would be much appreciated. And thank you in advance!
 
You should have this information:

(d/dt)Acceleration(t) = Velocity(t)
(d/dt)Velocity(t) = Displacement(t)

That's a good place to start.
 
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