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 t
hat 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.
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.
1 answer:
Answer:
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))
You might be interested in
So check the picture below
if we check the solutions or zeros for the equation, we get
and as you can see in the picture, the value of "x" when y = 3.5, or the height of the truck is
the truck, ends up with a clearance of
on either side, so, the maximum clearance, the truck can have, those two clearances added together, 
if we check the solutions or zeros for the equation, we get
and as you can see in the picture, the value of "x" when y = 3.5, or the height of the truck is
the truck, ends up with a clearance of