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 0 ft intially moving to the left 0.25 ft 0.1 Hz
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 0 ft intially moving to the left 0.25 ft 0.1 Hz
Solution Summary: The author calculates the displacement d as a function of time for an object that is attached to the horizontal spring of the subject.
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
0
ft intially moving to the left
0.25
ft
0.1
Hz
A spring with a spring constant k of 100 pounds per foot is loaded with 1-pound weight
and brought to equilibrium. It is then stretched an additional 1 inch and released. Find the
equation of motion, the amplitude, and the period. Neglect friction. Then
y(t)
c1cos(40sqrt2)t+c2sin(40sqrt2)t
where t is time in (seconds) and y(t) is displacement (in feet).
Amplitude: 1
inch(es)
Period: 2pi/(40sqrt(2))
second(s).
A motion detector monitors the horizontal position of the end of a clock's pendulum, p(t), in metres, at time t,
in seconds and it shows that the position function can be modelled by the function p(t) = 0.1 cos
4tt
3.
a) Determine the maximum speed achieved by the pendulum and the first time that it occurs. b) Determine the
max rate of change of the velocity and the time it happens. Round values to 3 decimal places.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.