Question

Select the correct answer. jackson is conducting an experiment for his physics class. he attaches a weight to the bottom of a metal spring. he then pulls the weight down so that it is a distance of 6 inches from its equilibrium position. jackson then releases the weight and finds that it takes 4 seconds for the spring to complete one oscillation. which function best models the position of the weight?

Answers

  1. The function that best models the position of the weight is s(t) = 6cos (pi/2*t).

    How to illustrate the function?

    From the information, we know that the spring is going to have a sin or a cos equation.
    We have that the maximum distance of the spring is 6 inches and it is achieved at t=0. We have that the function is of the form 6sin(at+B).
    We have that the period is 4 minutes and therefore that the time component in the equation needs to make a period (2pi) in 4 minutes.
    In general, a=2pi/T where a is this coefficient, T is the period. Finally, for B, since sin(pi/2)=1, we have that B=pi/2 because when t=0, we have that 6sin(B)=6.
    Substituting, we have s(t) = 6cos (pi/2*t).
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