11.1 - Simple Harmonic Motion
Get the Assessment: FA11.1.docx
Get the Example problems: Worksheet11.1-SHM.docx
1. An SHO with an amplitude of 0.470 m has a speed of 2.15 m/s when it is 0.230 m from equilibrium. What is its period? What is its position when it has a velocity of 1.10 m/s? What is its acceleration when it is at x = -0.370 m?
(1.20 s, 0.421 m, +10.2 m/s/s)
2. An SHO has an equation of position (in m) of x = 7.20sin(5.10t) What is its maximum velocity? What is its acceleration when it is at x = +4.20 m?
(36.7 m/s, -109 m/s/s)
3. Write the equation of position for an SHO that has an equation of velocity of v = 24.0cos(6.00t). What is its position and velocity at t = 11.2 s?
(x = 4.0sin(6.0t), -3.8 m, -8.1 m/s)
More Examples from the Practice sheet: (These are pretty hard)
4. An SHO has a mass of 3.61 kg, a period of 4.17 s, and a total energy of 15.7 J. What is its amplitude?
(1.96 m)
5. An SHO has a mass of 1.83 kg, a frequency of 10.0 Hz, and amplitude of 0.18 m. What is its potential energy when it is 0.13 m from equilibrium?
(61.0 J)
More Examples from the Practice sheet: (These are pretty hard)
Practice Problems SHM Problems from 11.1:
Speed, Amplitude, and Position:
1. An SHO has a period of 0.234 s and amplitude of 0.470 m. What is its speed and acceleration when it is at x = +0.118 m? (12.2 m/s, -85.1 m/s/s) 11 1 Examples #1
2. An SHO has a period of 3.45 s, and amplitude of 0.676 m. What is its distance from equilibrium when it has a speed of 0.645 m/s? (0.576 m) 11 1 Examples #2
3. An SHO has a speed of 0.627 m/s when it is 0.870 m from equilibrium. What is its period if its amplitude is 1.08 m? (6.41 s) 11 1 Examples #3
4. An SHO has a speed of 3.34 m/s when it is 0.540 m from equilibrium. What is its amplitude if its angular velocity is 7.50 rad/s? (0.700 m) <Video>
5. An SHO with an amplitude of 2.12 m has a speed of 5.86 m/s when it is at x = -1.80 m. What is its acceleration at this point? (+49.3 m/s/s) <Video>
Simple equations of motion:
6. An SHO has an equation of position (in m) of x = 14.0sin(6.50t) What is its acceleration at x = -8.00 m? (338 m/s/s) What is its position, velocity and acceleration at t = 3.20 s? (+13.0 m, -33.7 m/s, -549 m/s/s) 11 1 Examples #6
7. An SHO has an equation of position (in m) of x = 43.2sin(12.0t) What is its amplitude and angular velocity? (two questions) (43.2 m, 12.0 rad/s) 11 1 Examples #7
8. An SHO has an equation of position (in m) of x = 8.50sin(4.00t) What is its amplitude and maximum velocity? (8.50 m, 34.0 m/s) 11 1 Examples #8
9. An SHO has an equation of position (in m) of x = 9.50sin(1.62t) What is its position, velocity and acceleration at t = 9.25 s? (+6.29 m, -11.5 m/s, -16.5 m/s/s) <Video>
10. An SHO has an equation of velocity (in m/s) of v = 1.25cos(5.60t) What is its period? (1.12 s) What is its position, velocity, and acceleration at t = 4.60 s (+0.131 m , +1.01 m/s, -4.11 m/s/s) <Video>
Advanced Equations of motion:
11. An SHO has an equation of position (in m) of x = 5.10sin(6.35t). What is its acceleration when it is at x = +3.40 m? (-137 m/s/s) 11 1 Examples #11
12. An SHO has an equation of position (in m) of x = 3.50sin(11.0t) What is its velocity at t = 2.32 seconds? (+35.6 m/s) 11 1 Examples #12
13. An SHO that has an equation of position (in m) of x = 6.50sin(5.00t). What is its speed when it is 2.13 m from equilibrium? (30.7 m/s) 11 1 Examples #13
14. An SHO with a mass of 3.91 kg and an equation of velocity (in m/s) of v = 12.0cos(17.0t). What is its kinetic energy at t = 16.3 s? (181 J) What is its amplitude, and what is its acceleration at x = +0.600 m? (0.706 m, -173 m/s/s) 11 1 Examples #14
15. What is the amplitude of an SHO that has an equation of velocity (in m/s) of v = 14.0cos(5.70t). (2.46 m) What is the position at t = 16.9 s? (+2.14 m) <Video>
Energy
16. An SHO has a mass of 3.14 kg, a period of 4.32 s, and amplitude of 0.521 m. What is its total energy? (0.902 J) 11 1 Examples #16
17. An SHO has a mass of 2.61 kg, a period of 0.657 s, and a total energy of 843 J. What is its amplitude? (2.66 m) 11 1 Examples #17
18. An SHO has a mass of 6.67 kg, amplitude of 0.870 m, and a total energy of 18.3 J. What is its period? (2.33 s) <Video>
19. An SHO has a period of 3.41 s, and a total energy of 32.7 J, and amplitude of 5.43 m. What is its mass? (0.653 kg) <Video>
20. What is the period of a SHO that has a total energy of 24.2 J, a mass of 3.23 kg, and amplitude of 0.312 m? (0.506 s) <Video>
21. An SHO has a mass of 1.63 kg, a total energy of 45.7 J, amplitude of 0.148 m. What is its kinetic energy when it is 0.115 m from equilibrium? (18.1 J) 2025 Video #21 .:. 11 1 Examples #21
22. An SHO has a mass of 2.93 kg, a frequency of 12.0 Hz, and amplitude of 0.194 m. What is its potential energy when it is 0.120 m from equilibrium? (120. J) 2025 Video #22 .:. 11 1 Examples #22
23. An SHO has a mass of 4.20 kg, a total energy of 16.8 J, and amplitude of 0.840 m. What distance is it from equilibrium when it has a potential energy of 11.3 J? (0.689 m) 2025 Video #23 .:. 11 1 Examples #23
24. An SHO has a total energy of 436 J, a mass of 0.895 kg, and amplitude of 2.42 m. What is its speed when it is 1.21 m from equilibrium? (27.0 m/s) 11 1 Examples #24
25. An SHO has a total energy of 10.2 J, amplitude of 0.830 m, and a mass of 1.81 kg. What is its potential energy when its velocity is 2.28 m/s? (5.50 J) 11 1 Examples #25
More Problems Solved: (Simple Harmonic Motion worksheet) SHM Worksheet
The Instruction for this unit:
Kinematics:
Download the noteguide: Noteguide-SHM.docx
Video of Simple Harmonic Motion:
