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MATH1720HomeworkChapter4Section5

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Write the equation that describes the simple harmonic motion of a particle moving uniformly around a circle of radius  8 units, with angular speed  5 radians per second.
a.
s(t) =  5 sin  8t
c.
s(t) =  8 cos  5t
b.
s(t) =  8 sin  5t
d.
s(t) = sin  8t +  5
 

 2. 
Determine the period and frequency of oscillation when a pendulum of length  9 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.
a.
Period =  9ð sec, frequency = mc002-1.jpg cycles per sec
b.
Period = mc002-2.jpg sec, frequency = mc002-3.jpg cycles per sec
c.
Period = 2ðmc002-4.jpg sec, frequency = mc002-5.jpgmc002-6.jpg cycles per sec
d.
Period = 2ðmc002-7.jpg sec, frequency = mc002-8.jpgmc002-9.jpg cycles per sec
 

 3. 
Determine the length of a pendulum that has a period of  4 seconds.
a.
mc003-1.jpg ft
c.
mc003-3.jpg ft
b.
mc003-2.jpg ft
d.
mc003-4.jpg ft
 

 4. 
A spring with a spring constant of  5 and a 1-unit mass attached to it is stretched mc004-1.jpg and released. What is the equation for the resulting oscillatory motion?
a.
s(t) = mc004-2.jpg sin mc004-3.jpgt
c.
s(t) =  5 sin mc004-5.jpgt
b.
s(t) =  3 sin mc004-4.jpgt
d.
s(t) =  3 sin mc004-6.jpgt
 

 5. 
The formula for the up and down motion of a weight on a spring is given by mc005-1.jpg If the spring constant is  5, then what mass m must be used in order to produce a period of  6 seconds?
a.
mc005-2.jpg
c.
mc005-4.jpg
b.
mc005-3.jpg
d.
mc005-5.jpg
 

 6. 
The position of a weight attached to a spring is s(t) = -2 cos ( 6ð t) inches after t seconds. What is the maximum height that the weight rises above the equilibrium position?
a.
mc006-1.jpg in.
c.
mc006-2.jpgin.
b.
6 in.
d.
2 in.
 

 7. 
The position of a weight attached to a spring is s(t) = -3 cos  7t inches after t seconds. What are the frequency and period of the system?
a.
Frequency = mc007-1.jpg cycles per sec, period = mc007-2.jpg sec
b.
Frequency =  7 cycles per sec, period = mc007-3.jpg sec
c.
Frequency = mc007-4.jpg cycles per sec, period = mc007-5.jpg sec
d.
Frequency = mc007-6.jpg cycles per sec, period = mc007-7.jpg sec
 

 8. 
The position of a weight attached to a spring is s(t) = -5 cos  5ðt inches after t seconds. When does the weight first reach its maximum height?
a.
After mc008-1.jpg sec
c.
After mc008-3.jpg sec
b.
After mc008-2.jpg sec
d.
After mc008-4.jpg sec
 

 9. 
A weight attached to a spring is pulled down  4 inches below the equilibrium position. Assuming that the frequency of the system is mc009-1.jpg cycles per second, determine a trigonometric model that gives the position of the weight at time t seconds.
a.
s(t) =  4ð cos  5t
c.
s(t) =  4 cos  10t
b.
s(t) = -4 cos mc009-2.jpgt
d.
s(t) = -4 cos  10t
 

 10. 
A weight attached to a spring is pulled down  5 inches below the equilibrium position. Assuming that the period of the system is mc010-1.jpg sec, what is the frequency of the system?
a.
6 cycles per sec
c.
mc010-3.jpg cycles per sec
b.
mc010-2.jpg cycles per sec
d.
3 cycles per sec
 

 11. 
The position of a weight attached to a spring is s(t) = -5 cos  12ðt inches after t seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height? Round values to two decimal places, if necessary.
a.
The maximum height of  10 inches is first reached after  6 seconds.
b.
The maximum height of  5 inches is first reached after  6 seconds.
c.
The maximum height of  5 inches is first reached after  0.08 seconds.
d.
The maximum height of  10 inches is first reached after  3 seconds.
 

 12. 
A weight attached to a spring is pulled down  3 inches below the equilibrium position. Assuming that the period of the system is mc012-1.jpg second, determine a trigonometric model that gives the position of the weight at time t seconds.
a.
s(t) = -3cos  10ðt
c.
s(t) =  3cos  10ðt
b.
s(t) =  3cos mc012-2.jpgt
d.
s(t) = -3cos  5ðt
 

 13. 
A weight attached to a spring is pulled down  4 inches below the equilibrium position. Assuming that the frequency of the system is mc013-1.jpg cycles per second, determine a trigonometric model that gives the position of the weight at time t seconds.
a.
s(t) = -4cos 10t
c.
s(t) =  4cos 5t
b.
s(t) = -4cos 5t
d.
s(t) =  4cos 10t
 

 14. 
A guitar string is plucked so that it vibrates with a frequency of mc014-1.jpg Suppose the maximum displacement at the center of the string is mc014-2.jpg Find an equation of the form mc014-3.jpg to model this displacement. Round constants to 2 decimal places.
a.
s(t) =  1.16 cos  414.69t
c.
s(t) =  0.58 cos  10.50t
b.
s(t) =  0.58 cos  414.69t
d.
s(t) =  1.16 cos  10.50t
 

 15. 
Suppose that a weight on a spring has an initial position of mc015-1.jpg inches and a period of mc015-2.jpg Find a function mc015-3.jpg that models the displacement of the weight.
a.
s(t) =  -5 cos (2ð( 2.5)t)
c.
s(t) =  -10 cos (2ð( 0.4)t)
b.
s(t) =  -10 cos (2ð( 2.5)t)
d.
s(t) =  -5 cos (2ð( 0.4)t)
 



 
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