A pendulum is swinging next to a wall. The distance from the bob of the swinging pendulum to the wall varies in a periodic way that can be modeled by a trigonometric function.

The function has period 0.80.80, point, 8 seconds, amplitude 6 \text{ cm}6 cm6, start text, space, c, m, end text, and midline H = 15 \text{ cm}H=15 cmH, equals, 15, start text, space, c, m, end text. At time t = 0.5t=0.5t, equals, 0, point, 5 seconds, the bob is at its midline, moving towards the wall.

Find the formula of the trigonometric function that models the distance HHH from the pendulum's bob to the wall after t seconds. Define the function using radians.

  H(t) = 15 -6sin(2.5π(t -0.5))

Step-by-step explanation:

For midline M, amplitude A, period T and time t0 at which the function is decreasing from the midline, the function can be written as ...

  H(t) = M -Asin(2π/T(t -t0))

Using the given values of M=15, A=6, T=0.8 and t0 = 0.5, the equation is ...

  H(t) = 15 -6sin(2.5π(t -0.5))

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step-by-step explanation:

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