What is Harmonic motion: Definition and 1000 Discussions

In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion where the restoring force on the moving object is directly proportional to the object's displacement magnitude and acts towards the object's equilibrium position. It results in an oscillation which, if uninhibited by friction or any other dissipation of energy, continues indefinitely.
Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency. Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the displacement (and even so, it is only a good approximation when the angle of the swing is small; see small-angle approximation). Simple harmonic motion can also be used to model molecular vibration as well.
Simple harmonic motion provides a basis for the characterization of more complicated periodic motion through the techniques of Fourier analysis.

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  1. A

    Understanding Simple Harmonic Motion: Explained in Simple Terms

  2. A

    Simple Harmonic Motion Guitar String Question

    Homework Statement Question: "The midpoint of a guitar string oscillates with an amplitude of 2.24mm with a frequency of 400Hz. Calculate: i) The maximum speed at this point ii) The maximum acceleration of the string at this point" Homework Equations Suitable formulas: x=Asin(2*pi*f*t) ...
  3. P

    Simple Harmonic Motion: Why is acceleration positive at maximum displacement?

    For example, I have a pendulum with amplitude of 2m, when the pendulum is at a displacement of 2m, wouldn't the acceleration be negative as the restoring force is acting towards equilibrium? The equation I am taught is that maximum acceleration is (2*pi*frequency)^2 * amplitude, which is a...
  4. T

    Simple harmonic motion platform

    1. A platform is executing simple harmonic motion in a vertical direction with an amplitude of 5 cm and a frequency of 10/pi vibrations per second. a block is placed on the platform at the lowest point of its path. a) at what point will the block leave the platform? b)how far will the block...
  5. L

    Gravitational force in simple harmonic motion

    Homework Statement I am trying to derive the formula for simple harmonic motion of a mass hanging on a spring. I understand the derivation for the situation when the mass and the spring are on an horizontal table. Then I go about deriving the same formula for the situation when a mass is...
  6. H

    Simple Harmonic Motion Pendulum, can we use PE=1/2kAmplitude^2?

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  7. A

    Under-damped simple harmonic motion solution derivation

    I have learned in 1st year that the under-damped simple harmonic motion can be described by the differential equation m \frac {d^2 x} {dt^2} + b \frac {dx} {dt} + kx = 0 where m is the mass, b is the constant of linear drag and k is the spring constant But the derivation is skipped...
  8. N

    Is the propagation of a wave simple harmonic motion?

    Is the propagation of a wave simple harmonic motion? Simple harmonic motion is defined when the restoring force is proportional to the displacement. Hooke's Law F = -kx is an example. However at my level of understanding I have not yet read about the relationship between forces and waves and...
  9. 2

    Why is a pendulum only simple harmonic motion for small angles?

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  10. G

    Simple harmonic motion and circular motion

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  11. G

    Simple harmonic motion and positive constant w^2?

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  12. nomadreid

    Damped harmonic motion with one end without weight free

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  13. K

    Condition of simple harmonic motion

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  14. D

    Show that simple harmonic motion occurs

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  15. K

    Simple harmonic motion (direction of acceleration)

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  16. Rookie

    Harmonic Motion Spring Constant

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  17. A

    Introductory Simple Harmonic Motion Problem

    Q: When a sound wave with a certain intensity is detected by the tympanic membrane, the amplitude of the resultant motion is 1.0 nm (1.0 x 10-9 m). If the frequency of the sound is 600 Hz, what is the maximum speed of the membrane oscillation? My answer: 1)Vmax = wA (where w= angular velocity)...
  18. PsychonautQQ

    Energy in damped harmonic motion

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  19. M

    Show that the simple harmonic motion has a period

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  20. C

    Relationship between Simple Harmonic Motion Equation and Wave Equation

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  21. J

    Changing equilibrium point in damped simple harmonic motion

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  22. S

    Simple Harmonic Motion Pendulum

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  23. J

    Instantaneous response of damped simple harmonic motion

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  24. C

    Total distance in simple harmonic motion

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  25. Q

    Simple Harmonic Motion Displacement

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  26. G

    Simple Harmonic Motion: Calculate Max Velocity

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  27. jdawg

    Simple harmonic motion derivative of position function

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  28. I

    Spring and gravitational energies (Simple harmonic motion)

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  29. ThomasMagnus

    Simple Harmonic Motion Clarification

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  30. U

    Condition for Simple Harmonic Motion

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  31. R

    MHB Nonlinear oscillator and simple harmonic motion

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  32. Z

    Simple Harmonic Motion Problem

    Homework Statement An object moving with harmonic motion has an acceleration of -2 m/s^2 when the elongation is 0.5 m. Determine the angular frequency and the velocity and acceleration for t=1s. Homework Equations a=-ω2x (1) x=Acos(ωt+θ) (2) a=-Aω2cos(ωt+θ) (3) The Attempt at a...
  33. J

    Coverting Simple Harmonic Motion Equation to a Rotational Model

    Hi I am using Simple Harmonic Motion in a Matlab/Simulink model. Instead of using a motion for a simple pendulum, I decided to use a spring with a mass. The reasons for this is because my example is more like a lever attached to a pivot point and having an object at the end with a mass. A...
  34. M

    Harmonic Motion of Oscillating Particle

    Homework Statement A particle moves along the x axis. It is moving initially at the position 0.280 m, moving with velocity 0.200 m/s and acceleration -0.450 m/s^2. Suppose it moves with constant acceleration for 4.10 s. (a) Find the position of the particle after this time...
  35. C

    Damped simple harmonic motion experiment and questions?

    Homework Statement Hi, so my question is about a damped simple harmonic motion experiment The experiment is as follows: A 30 cm ruler with a needle attached to it is clamped to a bulldog clamp. The needle is placed in a beaker of water so that it is just inside the water ( by about...
  36. P

    Simple Harmonic Motion: Ball on Spring with Mass and Compression Calculation

    The problem is a ball is dropped onto a spring and the spring compresses .95m. The ball then sticks to the spring and oscillates with a period of 1.1 seconds and has a mass of 6kg. I thought that the equation mg(h+x)=1/2(k)(x^2) would be what i would use. I got h=.47m I also...
  37. N

    Exploring Simple Harmonic Motion: A=14cm, ω=3.0Hz

    Homework Statement Write a simple harmonic motion with amplitude 14cm , frequency 3.0Hz , and maximum displacement at t=0.The Attempt at a Solutiony (t) = A cos (ωt) = 14 cos (2πt/T) Dealing with angular frequency is easy. But deal with natural frequency throws me off course.
  38. W

    Simple Harmonic Motion Problem

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  39. P

    Simple Harmonic Motion amplitude problem

    Homework Statement An object is undergoing simple harmonic motion with frequency f = 3.1 Hz and an amplitude of 0.15 m. At t = 0.00 s the object is at x = 0.00 m. How long does it take the object to go from x = 0.00 m to x = 7.00×10-2 m. Homework Equations x(t)=Asin(ωt) The Attempt...
  40. C

    Why Do Harmonic Motion Equations Differ Across Sources?

    I was hoping that someone could explain why these different equations can be found from different sources please. The time dependent position, x(t), of an underdamped harmonic oscillator is given by: x(t)=e^{-\gamma t}acos(\omega_{1}t-\alpha) where \gamma is the damping coefficient, and...
  41. M

    How Can I Solve This Compound Harmonic Motion Problem with Different Methods?

    Homework Statement Determine the motion of this mechanical system satisfying the initial conditions :- y1(0) = 1 y2(0) = 2 y1'(0) = -2*sqrt(6) y2'(0) = sqrt(6) Hint : there are 4 different methods you can use to solve this problem. They all give the same exact result. I need to...
  42. P

    Simple Harmonic Motion: Simple Pendulum

    If we apply the small angle approximation so that a simple pendulum can be considered to be under going SHM, what kind of potential energy would the pendulum bob be having? If the answer is gravitational potential energy, then we have a contradiction because this would mean that the bob would...
  43. P

    Simple Harmonic Motion - Potential energy

    For a mass on a spring (vertical set up) why is potential energy U defined as 1/2 kx^2? This is just the elastic potential energy. Shouldn't it be U = 1/2 kx^2 + mgh? Both the elastic AND potential energy? Also, for a simple pendulum at a very low amplitude, the potential energy is all...
  44. P

    Simple Harmonic Motion - Mass on a Spring

    For a mass on a spring (vertical set up) undergoing SHM, we equate the restoring force, -kx, to -ω^2 x, coming to a conclusion that ω = \sqrt{\frac{k}{m}}. My question is, is the restoring force |mg - T| Where T is the tension in the spring? Because this seems to be the net force. I am used to...
  45. KiNGGeexD

    Simple harmonic motion (Again)

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  46. KiNGGeexD

    Simple Harmonic Motion (Total Energy)

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  47. R

    Interesting harmonic motion lab

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  48. L

    Simple Harmonic Motion vibrations

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  49. O

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  50. H

    Simple Harmonic Motion: Giancoli Problem Help

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