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. S

    Does Point A Oscillate in Simple Harmonic Motion with a Wave?

    you have a transverse sinusoidal wave on a string, and say there's a point A on that string. does point A oscillate in simple harmonic motion with a frequency that's equal to the frequency of the wave?
  2. B

    Finding the phase constant for simple harmonic motion

    Homework Statement I need to find the speed, at time t=0.015s, of a hydraulic valve component undergoing sinusoidal vibrations. The frequency of the vibrations is 25Hz, the amplitude is 2cm and the angular frequency is 157 s-1 Homework Equations The equation for speed of sinusoidal...
  3. T

    Simple Harmonic Motion Lab: Mass and Period Relationship Analysis

    Homework Statement Hi I just did a physics lab that involved a Simple Harmonic Motion. What I did was have a mass hung on a spring and then put different masses and find their Period (T) and time for 5 cycles going up and down. RESULTS: Mass (kg) 0.100 0.150 0.200 0.250 0.300...
  4. M

    Simple Harmonic Motion of a rolling ball

    Homework Statement A ball rolls on a circular track of radius 0.61 m with a constant angular speed of 1.3 rad/s in the counterclockwise direction. A. If the angular position of the ball at t= 0 is \theta= 0, find the x component of the ball's position at the time 2.6 s. Let \theta= 0...
  5. M

    Simple harmonic motion of a spring?

    Homework Statement I had a lab today and one of my questions is: "If you displace the end of the spring a little or a lot, in other words if you change the amplitude of the oscillation, the period will be the exact same. 1) How can this happen? 2) What is different about the motion of the...
  6. G

    Mathematica How do I fit damped harmonic motion data (x vs. t) using Mathematica?

    How do I fit the data given below into the standard form (ignore the part saying to use MathCad): http://screensnapr.com/u/apmqkd.png {{{0.002, 0.726}, {0.022, 0.739}, {0.042, 0.75}, {0.062, 0.759}, {0.082, 0.768}, {0.102, 0.776}, {0.121, 0.785}, {0.141, 0.794}, {0.161, 0.802}...
  7. B

    Simple harmonic motion - vibration frequency

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  8. C

    What is the Required Frequency for Simple Harmonic Motion Testing?

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  9. Telemachus

    Simple harmonic motion [ I have an exam tomorrow morning]

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  10. T

    Calculating Time for Simple Harmonic Motion: Rod with Freely Rotating Object

    Homework Statement Given a rod with length it is hinged thus it can freely rotate. An object is attached to the end of the rod and it is brought all the way vertically up. Then a slight disturbance and it flies down (from equilibrium). How long does it take for it to come down to the minimum...
  11. F

    Finding the variable S using the intercept in simple harmonic motion of spring.

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  12. F

    Simple Harmonic Motion Question

    Homework Statement Homework Equations x = A cos(wt-phi) The Attempt at a Solution Using the above equation for t, calculating values for t1 at -0.05 and t2 at 0.05, as well as assuming phase angle phi is zero, I get an answer of over 40 seconds. I think I may be using the wrong equation or...
  13. G

    Coulomb's Law and Simple Harmonic Motion

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  14. T

    Solving 2D Harmonic Motion Homework

    Homework Statement A particle undergoes simple harmonic motion in both the x and y directions simultaneously. Its x and y coordinates are given by x=asin(wt) y=bcos(wt) a. Eliminate t from these equations to show that the path of the particle in the x-y plane is an ellipse. b. Calculate...
  15. V

    Finding Velocity and Acceleration in Simple Harmonic Motion

    Please help me, Question The equation of motion of a mass is given as x = (0.2m) sin (3t). Find the velocity and acceleration of the mass when the object is +5cm from its equilibrium position.
  16. T

    Simple Harmonic Motion Homework: Finding Amplitude, Period, and Time of Travel

    Homework Statement A machaine part moves in a straight line with SHM. At positons 15mm and 20mm from the center of oscillation it has velocitys 2 m/s and 1 m/s respectively. find the amplitude and period of the motion. and the shortest time taken for the part to travel between these 2...
  17. C

    Show an electron is executing simple harmonic motion

    Homework Statement When the electron in a hydrogen atom bound to the nucleus moves a small distance from its equilibrium position, a restoring force at a given radius is given by: k = e^2/4*pi*epsilon*r^2 where r = 0.05 nm may be taken as the radius of the atom (the equilibrium radius of...
  18. H

    Simple Harmonic Motion of a Particle

    Homework Statement A particle is oscillating in simple harmonic motion with period 4.5 ms and amplitude 3.0 cm. At time t = 0, the particle is at the equilibrium position. Calculate, for this particle: a) frequency b) the angular frequency c) the maximum speed d) the maximum acceleration e)...
  19. J

    Simple Harmonic Motion, object floating in a liquid

    (apologies for the formatting, mixing LaTeX and regular text looks ugly, but I don't know how to do it otherwise) Homework Statement This is problem 3-7 from Thornton and Marion's Classical Dynamics. A body of uniform cross-sectional area A = 1 cm2 and of mass density \rho=0.8 g/cm3 floats...
  20. J

    Maximum Amplitude for Simple Harmonic Motion with Friction

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  21. G

    Mechanics problem about simple harmonic motion

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  22. M

    Graph of simple harmonic motion

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  23. M

    Kinematics: simple harmonic motion

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  24. P

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  25. M

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  26. S

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  27. C

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  28. F

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  29. P

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  30. S

    Dynamics/ Simple Harmonic motion help

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  31. C

    Conceptual simple harmonic motion question

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  32. S

    Simple harmonic motion (finding omega)

    Homework Statement A particle executes simple harmonic motion with an amplitude of 2.51cm. At what positive displacement from the midpoint of its motion does its speed equal one half of its max speed? Homework Equations A=2.51 cm x(t) = Acos(wt) v(t) = -Awsin(wt) vmax = |-Aw| The...
  33. S

    Simple harmonic motion block question

    Homework Statement A block of unknown mass is attached to a spring of spring constant 6.7N/m and undergoes simple harmonic motion with an amplitude of 7.8 cm. When the mass is halfway between its equilibrium position and its max endpoint, its speed is measured to be 38.5 cm/s. (a) Calculate...
  34. M

    Coulomb's Law and simple harmonic motion

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  35. M

    Simple Harmonic Motion of a spring

    Homework Statement A hanging spring stretches by 35.0cm when an object of mass 450g is hung on it at rest. In this situation we define its position as x=0. The object is pulled down an additional 18.0cm and released from rest to oscillate without friction. What is its position x at a moment...
  36. D

    Simple Harmonic Motion: Maximum Velocity and Acceleration Calculation

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  37. F

    Why Is My Calculation of Maximum Stretch in Simple Harmonic Motion Incorrect?

    Homework Statement A 50 g block is hung from a vertical spring. The spring constant is 4 N/m. We let go of the block when the spring is not stretched.What is the maximal stretch of the spring? 2. Equations Fs=k times x The Attempt at a Solution At the maximal stretch, the block is at...
  38. L

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  39. 1

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    hi i am having trouble grasping this question A block of mass M hangs from a rubber cord. The block is supported so that the cord is not stretched. The unstretched length of the cord is L0, and its mass is m, much less than M. The "spring constant" for the cord is k. The block is released and...
  40. R

    Simple Harmonic Motion of a table

    Homework Statement A table moves up and down in SHM of period 1 second. Find the amplitude it can have at which objects on the table just comence to lose contact with the table. The Attempt at a Solution How do I need to solve this problem? I'm only given the period from which I can...
  41. M

    Harmonic Motion: Calculating Speed in Simple Harmonic Motion

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  42. C

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  43. A

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    Homework Statement A mass on a spring obeys SHM.Given that the mass is initially at the equilibrium position,has an initial velocity of 2m/s,and a nastural frequency of 2 rad/s,Find A and φ After 13.2 sec what's the displacement of the mass Homework Equations ψ=Αcos(ωt+φ) The Attempt...
  44. L

    Solve Simple Harmonic Motion Homework for Mass m on Spring s

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  45. J

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    Homework Statement A 100 g ball attached to a spring with spring constant 2.9 oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = 4.8 cm. What is the ball's maximum acceleration? which I found to be amax= 180 cm/s^2 What is the ball's position when the...
  46. J

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  47. J

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  48. K

    Solving Simple Harmonic Motion Homework

    Homework Statement Please find the question in the attachment,i've attached it because it includes a graph Homework Equations a=-(omega)^2.x T=2.pie/omega Vmax=omega.A The Attempt at a Solution for part b i used the first equation a=-(omega)^2.x to find omega and then substituted...
  49. S

    Simple Harmonic motion with a compound mass spring system

    Homework Statement For my problem, I have two springs that have the same length, but different masses and spring constants. Both springs are secured at one end to a holder and at the other ends are connected to a single mass. My question is how do I find the angular velocity? Since the...
  50. P

    Simple Harmonic Motion - At which rate will a ball vibrate

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