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

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Homework Help Overview

The problem involves a mass suspended on a spring that oscillates, with its distance from the ceiling modeled by a cosine function. Participants are tasked with finding the height of point P from the ceiling and the rate of change of distance with respect to time.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the initial conditions of the problem, particularly the significance of the time variable t and the value of the cosine function at specific points. There is a focus on understanding the implications of the cosine function in the context of the problem.

Discussion Status

There is an active exchange regarding the initial release point and the value of the cosine function at t=0. Some participants affirm each other's observations about the cosine value and its relevance to the problem setup.

Contextual Notes

Participants are navigating the implications of the cosine function and its relationship to the initial conditions of the oscillation, with some confusion noted about the values involved.

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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!
 

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