For Exercises 47-48, a block is attached to a horizontal spring. At time t = 0 , if the block is moving to the left with an initial displacement of 0 ft , a maximum displacement of 1 3 and a frequency of 3 Hz , find a model for the displacement d as a function of time t .
For Exercises 47-48, a block is attached to a horizontal spring. At time t = 0 , if the block is moving to the left with an initial displacement of 0 ft , a maximum displacement of 1 3 and a frequency of 3 Hz , find a model for the displacement d as a function of time t .
Solution Summary: The author explains how to calculate the model for the displacement d as a function of time.
For Exercises 47-48, a block is attached to a horizontal spring.
At time
t
=
0
, if the block is moving to the left with an initial displacement of
0
ft
, a maximum displacement of
1
3
and a frequency of
3
Hz
, find a model for the displacement
d
as a function of time
t
.
The period T of a pendulum of length L is T = (2 √L)/√g, where g is the acceleration due to gravity. A pendulum is moved from the Canal Zone, where g = 32.09 feet per second per second, to Greenland, where g = 32.23 feet per second per second. Because of the change in temperature, the length of the pendulum changes from 2.5 feet to 2.48 feet. Approximate the change in the period of the pendulum
The pilot of a jet transport brings the engines to full takeoff before releasing the brakes as the aircraft is
standing on the runway. The jet thrust remains constant, and the aircraft has a near-constant acceleration of
0.4g. If the takeoff speed is 200 kph, calculate the distances and time from rest to takeoff.
A hot-air balloon is released at 1:00 P.M. and rises vertically at a rate of 6 m/sec. An observation point is situated 100 meters from a point on the ground directly below the balloon (see the figure). If t denotes the time (in seconds) after 1:00 P.M., use an equation to express the distance d between the balloon and the observation point in terms of t.
Thomas' Calculus: Early Transcendentals (14th Edition)
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