Question

A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t = 0 seconds. when the weight it released, it oscillates and returns to its original position at t = 3 seconds. which of the following equations models the distance, d, of the weight from its equilibrium after t seconds? d = negative 9 cosine (startfraction pi over 3 endfraction t) d = negative 9 cosine (startfraction 2 pi over 3 endfraction t) d = negative 3 cosine (startfraction pi over 9 endfraction t) d = negative 3 cosine (startfraction 2 pi over 9 endfraction t)

Answer 1

The equation which models the distance (d) of the weight from its equilibrium after time (t) is equal to d = -9cos(2π/3)t.

What is the period of a cosine function?

The period of a cosine function simply means the total length (distance) of the interval of values on the x-axis over which a graph lies and it's repeated.

Since the weight attached is at its lowest point at time (t = 0), therefore, the amplitude of equation will be negative nine (-9)

For the angular velocity at time period (t = 3s), we have:

ω = 2π/T

ω = 2π/3

Mathematically, the standard equation of a cosine function is given by:

y = Acos(ω)t

Substituting the given parameters into the formula, we have;

d = -9cos(2π/3)t.

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