Examples of
Frequency and Period Problems
Pendulum Problems
Spring Problems
Equations for Equation sheet for
Springs and Pendulum Problems
Examples of
Period
Frequency
Problems
Frequency and Period Problem
(Without Period or Frequency given)
Terry Jumps up and down on a
trampoline 30 times in 55 seconds.
What is the frequency with which he
is jumping?
30 times
55 seconds
0.55 Hz
Frequency and Period
Conversion problem
Terry Jumps up
and down on a
trampoline with
a frequency of
1.5 Hz. What is
the period of
Terry’s jumping?
1.5 Hz
0.67 sec
Examples of
Pendulum
Problems
Problem:
• At the California Academy of Sciences the
length of the pendulum is:
90m = L
• The acceleration of gravity at this location is:
9.8 m/s/s = g
• What is the Period?
T=???? seconds
Solution
Solve: “Plug and Chug”
List:
L = 90m
g = 9.8 m/s/s
T=???? seconds
90 m
9.8 m/s/s
9.18 s2
Choose equation:
(3.03 s)
(19.0 s)
A problem where you
Find the period or frequency 1st
A pendulum has a length of 3 m and
executes 20 complete vibrations in
70 seconds.
Find the acceleration of gravity at
the location of the pendulum.
A pendulum has a length of 3 m and
executes 20 complete vibrations in 70
seconds. Find g.
1.
f = cycles / seconds
= 20 cycles / 70 seconds
= 0.286 hz
= 0.286 / sec
2.
T=1/f
= (1 / 0.286) seconds
= 3.5 seconds
What short cut could I have
used?
# vibrations
# seconds is
the time for
all the
oscillations
L = 3m and T= 3.5 seconds
Find the acceleration of gravity at the location
3.5 s = 2π√(3/g)
3.5 s = 6.28 √(3/g)
Heads up!!
If you ÷ by 2π
 Use (2π ) !!
Square both sides
12.25 = 39.43 (3/g)
12.25 = 118.3/g
12.25(g) = 118.3
Divide by 12.25
g = 9.658 m/s/s
A problem Where
"g" = 9.8 m/s/s is “understood”
Know you use g=9.8 m/s/s if:
“g” not given or asked for used 9.8 m/s/s
Part 1: A simple pendulum has a period of 2.400
seconds where "g" = 9.810 m/s/s. Find the length?
Part 2: Find "g" where the period of the same
pendulum is 2.410 seconds at a different location.
Why are the items green on this problem??
Pendulum is not a variable,
why is it marked??
• A simple pendulum has a period of 2.400
seconds where "g" = 9.810 m/s/s. Find the
length?
• Find "g" where the period of the same
pendulum is 2.410 seconds at a different
location.
1st find the Length
A simple pendulum has a period of 2.400 seconds
where "g" = 9.810 m/s/s.
T2=4π2 (L/g)
• Write equation
2.4002=4 π2 (L/9.810) • Substitute #’s
2.4002= 39.44 (L/9.810)• Square 4 π2
2.4002(9.810) = L
•
÷ 39.44
And X 9.810
39.44
L=1.433 m
• Answer with
label
Part 2: Use Length from 1st part of problem
Same Pendulum, same length NOW:
Find "g" where the period of the pendulum is 2.410
seconds.
T2=4π2 (L/g)
2.4102= 4π2(1.433/g)
2.4102=39.44(1.433/g)
g 2.4102=39.44 (1.433)
g =39.44(1.433)/2.4102
g = 9.73 m/s/s
Equation
Substitute #’s
4 π2 =39.44
X by “g”
÷ 2.4102
Answer and
label
Examples of
Spring
Problems
Hooke’s Law
graphing
Examples of
using the graph
to find the Slope
and tHe vaLue of “k”
for springs
What is the spring
constant for the data
graphed below?
Δx(m)
y2 - y1
Slope =
(6,147)
k=
x2-x1
147N – 49N
6 m – 2m
(2,49)
(0,0)
k=
Δx(m)
How do I know the Label??
Labels on axes:
Rise (N) & Run (m)
So:
rise/run is N/m !!
98 N
4m
k = 24.5 N/m
Examples of
Spring
Problems
Using
Equations
Examples of
Hooke’s Law problems
Stretch or compress – at rest
In anticipation of her first game, Alesia pulls back
the handle of a pinball machine a distance of
5.0 cm. The force constant is 200 N/m. How
much force must Alesia exert?
Examples of Hooke’s Law problems
In anticipation of her first game, Alesia pulls back the handle of a pinball
machine a distance of 5.0 cm. The force constant is 200 N/m. How much
force must Alesia exert?
List:
Δx = 5.0 cm = .05 m
k = 200 N/m
Fsp=???
Fsp= k Δx
Fsp= 200N/m(0.05 m)
Fsp= 10N
Equation
Substitute #’s
Answer with label
Example of Oscillation spring
Problems
Oscillating or bouncing
• Bianca stands on a bathroom scale which
has a spring constant of 220 N/m. The
needle is bouncing from side to side.
Bianca’s mass is 180 kg. What is the period
of the vibrating needle attached to the
spring?
Example of Oscillation
Spring
Problem
List: k = 220 N/m
m = 180 kg
• Bianca stands on a bathroom scale
which has a spring constant of 220
N/m. The needle is bouncing from
side to side. Bianca’s mass is 180
kg. What is the period of the
vibrating needle attached to the
spring?
T = ??
0.818 s2
180 kg
(0.904 s)
220N/m
5.7 sec
Spring Problems
Use Both Equations
Example of Combination of
Hooke’s Law and Oscillation of spring
Find k from Hooke’s Law and then use the
oscillation equation
Autumn, a young 20 kg girl, is playing on a
trampoline. The trampoline sinks down 9 cm when
she stands in the middle. What is the spring
constant?
If the trampoline then begins to bounce, what would
the frequency of the bounces be?
Autumn, a young 20 kg girl, is playing
The PLAN:
on a trampoline. The trampoline sinks
Using
Hooke’s
Law
and
Oscillation
1st Find Force of Gravity on mass down 9 cm when she stands in the
of spring
middle. What is the spring
constant?
F2gnd= m
agk from Hooke’s Law
Find
If the trampoline then begins to
bounce, what would the frequency
of the bounces be?
List :
Fsp= k Δx
3rd use the oscillation equation to
find T
4th convert to Frequency
m = 20 kg
Δx = 9 cm = 0.09 m
f = ??
Using
Hooke’s Law & Oscillation of
spring
1st Find Force of Gravity on mass
Autumn, a young 20 kg girl, is playing
on a trampoline. The trampoline sinks
down 9 cm when she stands in the
middle. What is the spring
constant?
List :
m = 20 kg
Fg= m ag
Δx = 9 cm = 0.09 m
Fg= 20kg(-9.8m/s/s)
f = ??
Fg= - 196 N
Recall
From the FBD on the Lab
SO. . .
FS = + 196 N
Example of Combination of
Hooke’s Law and Oscillation of
spring
Autumn, a young 20 kg girl, is playing
on a trampoline. The trampoline sinks
down 9 cm when she stands in the
middle. What is the spring
constant?
2nd Find k from Hooke’s Law
List :
Fsp= k Δx
196 N =k(0.09m)
2180 N/m = k
m = 20 kg
Δx = 9 cm = 0.09 m
Fs= 196 N
f= ??
Example of Combination of
Hooke’s Law and Oscillation of
spring
Autumn, a young 20 kg girl, is playing on a
trampoline. The trampoline sinks down 9 cm
when she stands in the middle. What is the
spring constant?
3rd use the oscillation equation
to find T
If the trampoline then begins to bounce, what
would the frequency of the bounces be?
List :
m = 20 kg
Δx = 9 cm = 0.09 m
Fs= 196 N
k = 2180 N/m
20 kg
2180 N/m
T=
f = ??
(0.958 s)
.00917 s2
.602 sec
Example of Combination of
Hooke’s Law and Oscillation of
spring
Autumn, a young 20 kg girl, is playing on a
trampoline. The trampoline sinks down 9 cm
when she stands in the middle. What is the
spring constant?
If the trampoline then begins to bounce, what
would the frequency of the bounces be?
4th convert to frequency
List :
m = 20 kg
Δx = 9 cm = 0.09 m
Fs= 196 N
k = 2180 N/m
.602 s
T = 0.602 sec
f = ??
1.66 Hz
Spring Problems
4 part Spring problem
Use Fg to find the k value and then use same
string with same k to find 2nd mass.
If two “Grumpy Old Men” went ice fishing and were
comparing their fish with the extension of the same
spring, solve the following spring problem: “Grumpy
Sam” caught the first fish and magically realized the fish
had a mass of 23 kg. When this fish was suspended on
the spring, like the one we suspended masses on in lab,
the spring stretched so it was 3 cm longer than it was
without the fish. What is the spring constant for the
spring? “Grumpy Joe” then caught a fish that caused
the same spring to extend 5 cm from the length of the
empty spring,. What was the mass of “Grumpy
Joe’s” fish?
The Plan to solve:
Example of 4 part Spring problem
1st Use Fg to find the Force on the spring
2nd Use Hooke to find the k value
If two “Grumpy Old Men” went ice
fishing and were comparing their fish
with the extension of the same spring,
solve the following spring problem:
“Grumpy Sam” caught the first fish and
magically realized the fish had a mass
of 23 kg. When this fish was
suspended on the spring, like the one
we suspended masses on in lab, the
spring stretched so it was 3 cm longer
than it was without the fish. What is
the spring constant for the spring?
List :
3rd Same spring with same k to find 2nd Force
m = 23 kg
Fg= ??
Δx = 3 cm = 0.03 m
Fsp = ??
4th Convert weight to mass.
Examples of 4 part Spring problem If two “Grumpy Old Men” went ice
List :
m = 23 kg
Fg=
Δx = 3 cm = 0.03 m
Fsp =
fishing and were comparing their fish
with the extension of the same spring,
solve the following spring problem:
“Grumpy Sam” caught the first fish and
magically realized the fish had a mass
of 23 kg. When this fish was suspended
on the spring, like the one we
suspended masses on in lab, the spring
stretched so it was 3 cm longer than it
was without the fish. What is the
spring constant for the spring?
1st Use Fg to find the Force on the spring
Fg= m ag
Fg= 23kg(-9.8m/s/s)
- 225 N = - Fs
Fg= - 225 N
+ 225 N = + Fs
Examples of 4 part Spring problem If two “Grumpy Old Men” went ice
List :
m = 23 kg
Fg= - 225 N
Δx = 3 cm = 0.03 m
Fsp = 225 N
2nd use Hooke to find the k value
Fsp= k Δx
225 N =k(0.03m)
7500 N/m =k
fishing and were comparing their fish
with the extension of the same spring,
solve the following spring problem:
“Grumpy Sam” caught the first fish and
magically realized the fish had a mass
of 23 kg. When this fish was suspended
on the spring, like the one we
suspended masses on in lab, the spring
stretched so it was 3 cm longer than it
was without the fish. What is the
spring constant for the spring?
“Grumpy Joe’s” Fish
Examples of 4 part Spring problem
List :
NEW FORCE
m = ??? kg
NEW MASS
SAME SPRING!!
Fg= ???? N
Δx = 5 cm = 0.05 m
Fsp = ?? N
k = 7500 N/m
“Grumpy Joe” then caught a fish that
caused the same spring to extend 5 cm
from the length of the empty spring,.
What was the mass of “Grumpy
Joe’s” fish?
3rd same spring with same k to find other Force
Fsp= k Δx
Fsp = 7500N/m (0.05m)
Fsp = 375 N
Examples of 4 part Spring problem
List :
m = ??? kg
Fg= -375 N
Δx = 5 cm = 0.05 m
Fsp = 375 N
k = 7500 N/m
“Grumpy Joe’s” Fish
NEW FORCE
NEW MASS
SAME SPRING!!
“Grumpy Joe” then caught a fish that
caused the same spring to extend 5 cm
from the length of the empty spring,.
What was the mass of “Grumpy
Joe’s” fish?
4th convert weight to mass
Fg= m ag
- 375 N = - Fs
-375 N= m(-9.8m/s/s)
+ 375 N = + Fs
m= 38.3 kg
Equation
Sheet
Slides
for
Springs
and
Pendulums
Period and Frequency-notes
• Hertz is unit that means 1/sec
• Abbreviated ------- Hz
• Mega Hertz –FM radio Page 3 Space #4
• Kilo Hertz – AM radio
Period
# cycles
Hz
Sec-1
1/sec
# repetitions
f
# revolutions
Frequency
Period and Frequency
• Hertz is unit that means 1/sec
• Abbreviated ------- Hz
• Mega Hertz –FM radio Page 3 Space #5
• Kilo Hertz – AM radio
Period
Hz
f
Sec-1
1/sec
Frequency
Use when you
know
either T or f
Oscillations for Pendulums only-Notes
Length of the pendulum and gravity determine how fast
the pendulum oscillates back and forth.
Page 3 Space #6
Period
m/s/s
m/s2
Scalar-positive!!
Hz
Sec
-1
1/sec
All 3
equations
are the
same, just
re-arranged
Page 4 #1
Page 4 #2
Springs only
page 4 Space #3
Period and Frequency
• Hertz is unit that means 1/sec ( Hz)
Hooke’s Law for Springs only
Springs only