The Pendulum
Brought to you by Galileo
Galileo discovered that the time it takes for a pendulum takes to swing to and fro through small distances depends only on the length of the pendulum and the acceleration of gravity. This to and fro motion is called simple harmonic motion. This is for small angles only.
Pendulum Problems:
A. What is the period on Earth of a pendulum with a length of 2.4 m?
3.11s
B. How long should a pendulum be in order to swing back and forth in 1.6 s?
0.64m
C. A grandfather clock needs to have a period of one second. What length of pendulum should be hung for the clock to keep good time?
0.25m
D. If the clock from question 1 was taken to the moon where gravity is 1.7 m/s2, what length should the pendulum have?
0.043m
E. A mountain climber, who has had physics in high school, figures out the gravity at his location in the mountains. He used a 4.0 m length of string and found that with a rock tied at its end, its period as a pendulum was 4.1 seconds. What was g at his location?
9.39m/s2
F. A ride at 6 Flags straps you in and you swing like a pendulum. The length of the cord that holds you is about 20 meters. How much time does it take to swing back and forth once?
8.98s
G. A playground swing is 3 meters long. What is the period of the swing?
3.48s
H. If we colonized Mars and took the swing-set from question 5 there, it would swing back and forth with a period of 5.7 seconds. What is the acceleration due to gravity on mars?
3.65m/s2
I. The desk toy with the swinging ball bearings has a length of 12 cm. What is the period of their swing?
0.7s
J. A pendulum is 0.75 meters long and has a period of 4.17 seconds. Is this pendulum on the earth, moon, or mars? Do a calculation to prove your answer.
g=1.7m/s2, moon!
K. You decide to design a pendulum to be used on March. What chord length should you choose if you want the period of the pendulum to be 1.0s The acceleration due to gravity on March is 3.72 m/s2
0.094m
L. Samira measures the period of a swing on a playground, using her mobile phone. Ten periods takes 27.56s. What is the length of the swings ropes?
1.89m
M. The period of a pendulum is T seconds. When the chord is extended by 30cm the period of the pendulum increases by 30 %. What was the length of the chord from start?
0.43m
N. Use the pendulum equation to determine the length of pendulum that has a period of 4seconds.
3.97m
O. In 1851, the French physicist Jean Foucault hung a large iron ball on a wire about 61 m (200ft) long to show that the Earth rotates. The pendulum appears to swing in different directions as the Earth turns under it. Calculate the swinging frequency of this pendulum.
0.064Hz
P. A geologist finds that the frequency of a pendulum is 0.3204 Hz when at a location where the acceleration of gravity is 9.80 m/s2. What is the value of g at a location where the pendulum’s frequency is 0.3196 Hz?
9.75m/s2
Q. The frequency of a pendulum is 39% less when on the surface of Mars than when on the Earth’s surface. Use this fact to calculate the acceleration of gravity on Mars.
3.64m/s2
R. A pendulum with a string of length .2m is displaced 6cm to the right. Find its position after 8 seconds.
5.12cm
S. A pendulum with a string of length 40cm is displaced 5cm to the right. Find its position after 2 seconds.
-4.45cm
T. A pendulum with a string of length 50cm has a displacement of -8cm after 4 seconds. Find its initial displacement.
-19.2cm
U. A pendulum with a string of length 21cm has a displacement of 2cm after 10 seconds. Find its initial displacement
2.88cm
V. A pendulum has an initial displacement of 10cm and is found to be at a position of 2cm after 1.5 seconds. Find the length of the string.
11.76m
W. A pendulum has an initial displacement of 6cm and is found to be at a position of -5cm after 1 second. Find the length of the string.
1.5m
X. A pendulum with a string of length 34cm has an initial displacement of 6cm. After a certain time, it is observed to be at -3cm. Find one possibility for the time at that position.
0.39s
Y. A pendulum with a string of length 91cm has an initial displacement of 8.5cm. After a certain time, it is observed to be at -4cm. Find one possibility for the time at that position.
0.63s
Z. A pendulum with a string of length 60cm is displaced 6cm to the right. Find its position after a minute.
-5cm
Springs
A. A 3kg mass is placed on a spring with a spring constant of 60N/m. Find the expansion (x) of its equilibrium position.
0.49m
B. A 17kg mass is placed on a spring with a spring constant of 1200N/m. Find the expansion (x) of its equilibrium position
0.14m
C. What is the force constant of a Hooke’s Law spring if the extension of the spring is 0.15 m when a mass of 0.75kg is placed on it?
49N/m
D. What is the force constant of a Hooke’s Law spring if the extension of the spring is 6cm when a mass of 2kg is placed on it?
326.7N/m
E. A mass is placed on a Hooke’s Law spring where k=1000N/m and stretched it 18cm. What is the mass?
18.37kg
F. A mass is placed on a Hooke’s Law spring where k=550N/m and stretched it 4cm. What is the mass?
2.24kg
G. Calculate the period for a spring whose force constant is 15 N/m, if the mass on the spring is 1.0kg
1.6s
H. Calculate the period for a spring whose force constant is 300N/m, if the mass on the spring is 0.5kg
0.26s
I. Find the frequency of a spring with a k=300 N/m and a mass of 200 g suspended from it.
6.16Hz
J. Find the frequency of a spring with a k=400 N/m and a mass of 50g suspended from it.
14.24Hz
K. Find the frequency of a spring where k=1200N/m and a mass of 1kg is suspended from it.
5.51Hz
L. Find the displacement of a mass of 15g after 3 seconds if the initial displacement is 4cm and the spring constant is 75N/m
0.30cm
M. Find the displacement of a mass of 1kg after 6 seconds if the initial displacement is 10cm and the spring constant is 500N/m
-6.37cm
N. Find the displacement of a mass of 30grams after 2 seconds if the initial displacement is 0.16m and the spring constant is 600N/m
0.1592m
O. A 1.3kg mass is placed on a spring and allowed to come to rest, stretching 6cm. It is then displaced an additional 5cm. Find its period.
0.41s
P. A 0.5kg mass is placed on a spring and allowed to come to rest, stretching 15cm. It is then displaced an additional 16cm. Find its period.
0.734s
Q. A 12kg mass is placed on a spring and allowed to come to rest, stretching 10cm. It is then displaced an additional 12cm. Find its frequency.
1.58Hz
R. A 40g mass is placed on a spring and allowed to come to rest, stretching 3cm. It is then displaced an additional 4cm. Find its frequency
2.88Hz
S. A 60g mass is placed on a spring and allowed to come to rest, stretching 1.4cm. It is then displaced an additional 10cm. Find its position after 2 seconds.
-8.82cm
T. A1kg mass is placed on a spring and allowed to come to rest, stretching 3cm. It is then displaced an additional 5cm. Find its position after 10 seconds.
0.6267cm
U. A 1kg pass is placed on a spring and allowed to come to rest, stretching 0.5cm. It is then displaced an additional 1cm. Find the time where it will return to this same displacement.
0.142 seconds
V. A 6kg mass is placed on a spring and allowed to come to rest, stretching 5cm. It is then displaced an additional 12cm. Find the time where it will return to this same displacement.
0.45 seconds
W. A mass on a spring is initially displaced 10cm. After 0.5 seconds it is at -5cm. Find its frequency.
0.67Hz
X. A mass on a spring is initially displaced 8cm. After 1 second it is at a 1cm. Find its frequency.
0.234Hz
Y. A mass on a spring is initially displaced 6cm. After 5 seconds it is at -5cm. Find its period.
12.29s
Z. A mass on a spring is initially displaced 2cm. After 0.25 seconds it is at -1.5cm. Find its period.
0.65s