For Exercises 15-22, suppose that an object is attached to a horizontal spring subject to the given conditions. Find a model for the displacement d as a function of the time t . (See Example 1) Initial Displacement d at t = 0 Amplitude Period or Frequency 2.5 in . 2.5 in . 1.2 sec
For Exercises 15-22, suppose that an object is attached to a horizontal spring subject to the given conditions. Find a model for the displacement d as a function of the time t . (See Example 1) Initial Displacement d at t = 0 Amplitude Period or Frequency 2.5 in . 2.5 in . 1.2 sec
For Exercises 15-22, suppose that an object is attached to a horizontal spring subject to the given conditions. Find a model for the displacement
d
as a function of the time
t
. (See Example 1)
Initial Displacement
d
at
t
=
0
Amplitude
Period or Frequency
2.5
in
.
2.5
in
.
1.2
sec
e An airplane flying on a straight flight path will be exactly above a radar tracking
station, which is 5,000 km below the path. When the distance of the plane from the
station is 40,000 km, this distance decreases at the rate of 8,000 km/hr. At what rate is
the plane flying at that instance?
novi
f. A truck travelling southwards at 40 kph and a car traveling eastward at a rate of 60 kph
are headed for an intersection. At what rate are the vehicles approaching each other
when the truck is 1 km from the intersection while the car is 2 km from the
intersection?
g. Water is being poured at the rate of 5 m³/sec into an inverted conical tank of radius
10 m and altitude 20 m. How fast is the water level rising when the water level is at
8 m? (Note: Here you will be using the concepts of similar triangles in order to rewrite
the radius in terms of the height.)
itoun bont
h. A particle is moving along the curve with equation y = 3-x. At the point (2, 1), it
was observed that the x-coordinate…
A force of 15 Newtons stretches a spring 20 centimeters. After a 3 kilogram mass is attached
to the spring, the mass is pulled down to a position √3 meters below equilibrium and released
with an upward velocity of 5 meters per second. Find
a. The equation of motion.
b. The amplitude, period, and phase shift of the simple harmonic motion.
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