A block hangs on a spring attached to the ceiling and is pulled down 8 in. below its equilibrium position. After release, the block makes one complete up-and-down cycle in 1.2 sec and follows simple harmonic motion. a. Write a function to model the displacement d (in inches) as a function of the time d (in seconds) after release. Assume that a displacement above the equilibrium position is positive. b. Find the displacement of the block and direction of movement at t = 0.3 sec .
A block hangs on a spring attached to the ceiling and is pulled down 8 in. below its equilibrium position. After release, the block makes one complete up-and-down cycle in 1.2 sec and follows simple harmonic motion. a. Write a function to model the displacement d (in inches) as a function of the time d (in seconds) after release. Assume that a displacement above the equilibrium position is positive. b. Find the displacement of the block and direction of movement at t = 0.3 sec .
Solution Summary: The author compares the quantities with the actual function, that is, d=Amathrmcos5pi 3t.
A block hangs on a spring attached to the ceiling and is pulled down 8 in. below its equilibrium position. After release, the block makes one complete up-and-down cycle in
1.2
sec
and follows simple harmonic motion.
a. Write a function to model the displacement
d
(in inches) as a function of the time
d
(in seconds) after release. Assume that a displacement above the equilibrium position is positive.
b. Find the displacement of the block and direction of movement at
t
=
0.3
sec
.
A rotating light is located 13 feet from a wall. The light completes one rotation every 3 seconds. Find the
rate at which the light projected onto the wall is moving along the wall when the light's angle is 15
degrees from perpendicular to the wall.
wall
T
light
feet per second
Answer is a positive value. Give your answer accurate to at least one decimal place.
A TV camera is situated 100 m from the site of the Endeavour launch. The
rocket's elevation t seconds after liftoff is s = 200f“ . How rapidly must the
camera angle increase in order to maintain a view of the rocket 5 seconds of.
2.
liftoff?
Thomas' Calculus: Early Transcendentals (14th Edition)
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