Calc/Trig Hybrid Homework: Find P's Height & ds/dt

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Homework Statement



A mass is suspended from the ceiling on a spring. It is pulled down to point P and then released. It oscillates up and down. Its distance, s cm, from the ceiling, is modeled by the function s=48 + 10cos(\Pit) where t is the time in seconds from release.

(a)What is the distance of the point P from the ceiling. Do not use a calculator

(b) Find ds/dt

Homework Equations



The Unit Circle

The Attempt at a Solution



(a) I set it equal to zero, and then used the unit circle to find that cos(\Pi) = 1, but that doesn't take into account the t.
 
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The "point of initial release" is where t=0 isn't it? Besides cos(pi)=(-1).

Signed, Confused.
 
Last edited:
Dick said:
The "point of initial release" is where t=0 isn't it? Besides cos(pi)=(-1).

Signed, Confused.

Oh, you're right about cos(pi)=(-1)
 
He's also right about the mass being at point P when t= 0!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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