SHM Springs
1. A mass oscillates with a period of 1.6 seconds when attached to a spring (k = 25 N/m.). What is the mass?
[1.6 kg]
2.
What will be the period of a 3 kg mass oscillating on a spring with a k = 210 N/m? The frequency?
[0.75 s, 1.33 Hz]
3.
A 5.4 kg mass oscillates with a frequency of 10 Hz. What is the period? What must be the spring constant?
[0.1 s, 21,300 N/m]
4.
If k = 75 N/m . How far will the spring stretch when the mas is hung from it?
x
0.35 kg
[4.5 cm]
5.
A 0.75 kg mass is placed on s spring and it stretches it 0.085 m.
A. What is the spring constant? [86 N/m]
B. How much potential energy is stored in the spring? [0.31 J]
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6.
A 65 kg physics student is laying on a trampoline (acts like a spring). He/she is oscillating with a frequency of 0.75 Hz. What
is the spring constant of the trampoline?
[1400 N/m]
7.
A 1.5 kg object is undergoing SHM with amplitude of 0.010 m and a frequency of 8.0 Hz.
A. What is the period of the object? [0.13 s]
B. What is the spring constant of the system? [3800 N/m]
C. What will be the maximum velocity of the object? [0.5 m/s]
D. How long will it take to travel from one end to the equilibrium position? [0.031 s]
8.
A 2.5 kg mass on a spring (k = 350 N/m) oscillates with a maximum speed of 0.80 m/s.
A. What is the amplitude of the motion? [0.068 m]
B. What is the period of the motion? [0.53 s]
C. What will be the maximum energy of the system? [0.80 J]
[11.5 J]
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9.
What is the total energy of a 2.4 kg object that is oscillating between -0.075 m and +0.075 m at 6.5 Hz?
10. A 900 kg car strikes a huge spring traveling at 22 m/s and compresses it 5.0 m.
A. What is the spring constant of the spring? [17,400 N/m]
B. How long will the car be in contact with the spring? [0.713 s]
11. An object undergoes SHM according to the following equation:
x = (0.30m) cos(8.0t )
A. What is the object’s amplitude? [0.30 m]
B. What is the object’s frequency? [1.27 Hz]
C. What are the maximum velocity and acceleration of the object? [v = ±2.4 m/s, a = ±19 m/s2]
12. An object undergoes SHM according to the following equation:
v  (5) sin(10t )
A. What is the object’s amplitude? [0.5 m]
B. What is the object’s frequency? [1.6 Hz]
C. What are the maximum velocity and acceleration of the object? [v = ±5 m/s, a = ±50 m/s2]
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13. Use the graph to find:
A. The period. [4 s]
B. The . [1.57 rad/s]
C. The maximum velocity of the object. [4.71 m/s]
D. The spring constant if the object is 4.5 kg. [11.1 N/m]
14. Use the graph to find:
A. The period. [0.8 s]
B. The amplitude. [2.55 m]
C. The maximum acceleration [157 m/s2]
D. x when t = 4.3 s. [-1.8 m]
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15. A mass m has an  = 2.3 Hz when attached to spring that has a k = 65 N/m. What is m? How far will it stretch the spring if
the mass is hung from the spring?
[m = 12.3 kg, x = 1.85 m]
16. A 2.0 kg fish stretches a spring scale 3.5 cm. It is then pulled down another 1.0 cm and released. What will be the frequency
of the fish as it bobs up and down?
[2.7 Hz]
17. A spring stretches 0.150 m when a 0.30-kg mass is hung from it. The spring is then stretched an additional 0.100 m from this
equilibrium point and released. Determine (a) the spring constant k, (b) the maximum velocity v max, and (c) the maximum
acceleration of the mass.
[k = 19.6 N/m, vmax = 0.808 m/s, amax = 6.52 m/s2]
18. If a particle under SHM with amplitude A, what is the total distance it travels in one period?
[4A]
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19. A fisherman’s scale stretches 2.5 cm when a 2.1-kg fish hangs from it. What is the spring constant and what will be the
frequency of vibration if the fish is pulled down and released so that it vibrates up and down?
[k = 823 N/m, f = 3.15 Hz]
20. A 0.350-kg mass at the end of a spring has a frequency of 2 Hz with an amplitude of 0.12 m. Determine (a) the velocity when
it passes the equilibrium point, (b) the total energy of the system.
[v = 1.5 m/s, Energy = 0.40 J]
21. An object with a mass of 0.500 kg is undergoing simple harmonic motion on the end of a horizontal spring with force constant
k = 400 N/m. When the object is at the center, it is observed to have a speed of 0.300 m/s. What is (a) The total energy of the
object at any point of its motion? (b) The amplitude of the motion? (c) The maximum acceleration attained by the object
during its motion?
[Energy = 0.023 J, A = 0.011m, 8.5 m/s2]
22. A harmonic oscillator is made using a block with mass 0.500 kg and a spring with unknown force constant. The oscillator is
found to have a period of 600 s, find the force constant (k) of the spring.
[0.000055 N/m]
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23. An object with a mass of 4.00 kg is attached to a spring with force constant k = 100 N/m. The object is given an initial
velocity in the positive direction of magnitude of vo=9.00 m/s and no initial displacement (x0 = 0). Find (a) the amplitude; (b)
the time it would take to travel from one end to the middle, (c) the total energy of the motion.
[A = 1.8 m, 0.314 s, 162 J]
24. Us the graph to answer the questions:
0.7 m
-0.7 m
3s
A.
B.
C.
D.
6s
9s
The amplitude. [0.7 m]
The period. [3 s]
The frequency. [0.33 Hz]
Maximum velocity? [1.45 m/s]Maximum acceleration? [3.0 m/s2]
25. Use the graph to answer the questions (mass of object is 3 kg and k = 250 N/m):
8 m/s
-8 m/s
A. What is the maximum velocity? [8 m/s]
B. What is the period? [0.69 s]
C. What is the amplitude? [0.87 m]
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26. Given the following acceleration graph, what is the period if the amplitude is 0.75 m?
30 m/s2
-30 m/s2
[0.99 s]
Challenge Problem
27. A mass m on a spring vibrates with a frequency of 2.0 Hz. When 0.75 kg is added to the mass the frequency becomes 1.4 Hz.
What is the value of m? (hint: same k for both)
[m = 0.72 kg]
SHM Pendulums:
28. What is the period of the pendulum whose length is 0.75 m?
[1.7 s]
29. A pendulum has a frequency of 1.0 Hz. What must be the length of the pendulum?
[0.25 m]
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30. An astronaut takes a 1.5 m pendulum to the surface of Mars and observes it to have a period of 4.0 s. What is the value of g
on mars?
[3.7 m/s2]
31. A 2.5 m long pendulum makes 5 complete swings (other side and back) in 16 s. What is the value of g where the pendulum is
located?
[9.6 m/s2]
32. The Burj Khalifa in Dubai is the tallest building in the world (828 m). What would be the period of a pendulum hung from its
top?
[57.8 seconds]
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33. Pendulum A has a period that is 20% more than pendulum B. Which pendulum has a greater length? How much longer is it?
[Pendulum A is 1.44 times longer]
34. Pendulum C has a period that is 30% less than pendulum D. Which pendulum has a greater length? How much longer is it?
[Pendulum D is 2.04 times longer]
35. A 4 m long pendulum on Earth is set in motion.
A. What is its period?
B. What will be the highest (above the center) it will go on either side if its velocity in the center is 2 m/s?
A. [4.01 s]
B. [0.2 m]
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