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It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches. which function models the horizontal displacement as a function of time in seconds?

Respuesta :

MrRoyal

The function that models the horizontal displacement as a function of time in seconds is y = 5cos(2Ï€/3 x)

How to model the function?

The given parameters are:

  • Time, t = 1.5 seconds
  • Horizontal distance, h = 10 inches

Start by calculating the amplitude, A using:

A = h/2

This gives

A = 10/2

A = 5

Next, we calculate the period using:

B = π/t

This gives

B = π/1.5

Evaluate

B = 2Ï€/3

The pendulum is at the middle.

So, it has no vertical displacement

The function is then represented as:

y = Acos(Bx)

This gives

y = 5cos(2Ï€/3 x)

Hence, the function that models the horizontal displacement as a function of time in seconds is y = 5cos(2Ï€/3 x)

Read more about cosine functions at:

https://brainly.com/question/17075439

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