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. D

    Frame of reference in a simple harmonic motion vertical spring

    I have doubts of how can I put my frame of reference in a simple harmonic motion vertical spring. Normally the books choose the origin in the equilibrium position and the positive distance (x>0) downward, and in this conditions Newton´s second law is: ma=-kx; but instead of putting the positive...
  2. K

    The Importance of Damping in Simple Harmonic Motion Explained

    I need help for the second part please. How do the oscillations being damped prevent them from being S.H.M. as well the other 2 points? I need an explanation so I can understand. The oscillations would still have the same time period eve if they are damped. Low frequency due to...
  3. T

    Simple Harmonic Motion: Amplitude of Oscillation for a Spring System

    Homework Statement The masses in figure slide on a frictionless table.m1 ,but not m2 ,is fastened to the spring.If now m1 and m2 are pushed to the left,so that the spring is compressed a distance d,what will be the amplitude of the oscillation of m1 after the spring system is released...
  4. L

    Harmonic motion and acceleration

    A system exhibits simple harmonic motion with a frequency of 0.85 cycles per second. Calculate the acceleration experienced by the mass 3.0 m from the equilibrium This question seems simple, I haven't really tried anything cause I can't figure out how to start. I need help to start this...
  5. L

    Queries on Damped Harmonic Motion

    So we know that SHM can be described as: x(t) = Acos(ωt + ϕ) v(t) = -Aω sin(ωt + ϕ) a(t) = -Aω^2 cos(ωt + ϕ) it can be easily said that the max acceleration (in terms of magnitude) a SHM system can achieve is Aω^2 In Damped Harmonic Motion we know that: x(t) = (A)(e^(-bt/2m))cos(ωt + ϕ) given...
  6. D

    Simple harmonic motion of two solid cylinders attached to a spring

    Homework Statement ) Two uniform, solid cylinders of radius R and total mass M are connected along their common axis by a short, massless rod. They are attached to a spring with force constant k using a frictionless ring around the axle. If the spring is pulled out and released, the cylinders...
  7. S

    Simple harmonic motion of a charged particle in a rod

    Homework Statement Two points, each of charge Q, are fixed at either end of a frictionless rod of length 2R. Another point charge, of charge q (not Q) is free to move along the rod. Show that if charge q is displaced a small distance x (0<x<<R) from the centre of the rod, it will undergo...
  8. G

    Simple Harmonic Motion Equilibrium

    I am a little confused with this subject. If you have a mass hanging from a spring, there is a specific equilibrium point, but what if you apply a force downwards on the mass, will this have an effect on the equilibrium position or will it remain the same? thanks!
  9. I

    Simple Harmonic Motion: Pendulum theory, trouble understanding

    Homework Statement So with pendulums in SHM, in my A level physics textbook (AQA Physics A), it shows a pendulum that has been displaced from equilibrium. It says that the restoring force is provided by the object's weight. Why isn't the restoring force provided by the tension in the string...
  10. H

    Simple harmonic motion equations derivation?

    Well I was going through class lecture notes and my professor wrote this When x = A(the maximum value), v=0: E=1/2kA^2 When v = wA, x=0: E=1/2mw^2A^2 where w = omega, A = amplitude, k = spring constant, m = mass, v = velocity and apparently both equations are equal, i would like to...
  11. C

    What Would a Pendulum's Period Be on the Moon?

    Homework Statement if a pendulum has a period of .36s on Earth, what would its period be on the moon Homework Equations T=2pi sqrt l/g The Attempt at a Solution How do u go about solving thAt without length?
  12. P

    Calculating the Period of Oscillation for a Mass Attached to a Spring

    Homework Statement Mass = 2.4 kg spring constant = 400 N/m equilbrium length = 1.5 The two ends of the spring are fixed at point A, and at point B which is 1.9m away from A. The 2.4 kg mass is attached to the midpoint of the spring, the mass is slightly disturbed. What is the period of...
  13. L

    Calculating Static Spring Deflection in Basic Harmonic Motion

    A 10kg mass is suspended from a spring which has a constant K = 2.5kn/m. At time t=0, it has a downward velovcity of 0.5m/s as it passes through the position of static equilibrium. Determine the static spring deflection. I believe i first need to calculate the force which requires basic...
  14. K

    Simple Harmonic Motion (Pendulum)

    Homework Statement Two pendula of length 1.00m are set in motion at the same time. One pendula has a bob of mass 0.050kg and the other has a mass of 0.100kg. 1. What is the ratio of the periods of oscillation? 2. What is the period of oscillation if the initial angular displacement is...
  15. T

    How is the angular momentum related to x and y coordinates in SHM?

    Homework Statement Two-dimensional SHM: A particle undergoes simple harmonic motion in both the x and y directions simultaneously. Its x and y coordinates are given by x = asin(ωt) y = bcos(ωt) Show that the quantity x\dot{y}-y\dot{x} is also constant along the ellipse, where here the...
  16. R

    Simple Harmonic Motion of a Spring

    So over the weekend my physics prof has assigned an assignment where one of the questions is as follows and here is my thought process: A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yi such that the...
  17. A

    Alternating Current and Simple Harmonic Motion

    Hello, I was being taught AC in High School, It was good but the way they taught us DC, things like drift velocity, no of electrons per unit volume etc, it was easy to visualize electrons rushing in a conductor. I tried to visualise AC(which was not taught to us) and I came to a conclusion...
  18. S

    Simple Harmonic Motion Energy Problem

    Homework Statement Derive the equilibrium state of a simple harmonic oscillation and show that the derivative of the maximum displacement is s^{'} = 2 \sqrt{E} Homework Equations F = -k x The Attempt at a Solution m a = -k s \rightarrow ms^{''}...
  19. S

    Simple Harmonic Motion: Period Calculation and Newton's Second Law Explanation

    Homework Statement A spring is freely hanged on a ceiling. You attach a mass to the end of the spring and let the mass go. It falls down a distance of 49 cm and comes back to where it started. It contineous to oscillate in a simple harmonic motion going up and down - a total distance of 49...
  20. O

    Simple harmonic motion function

    Hello, When doing problems with SHM, my textbook says something like: An object in vertical shm is described by <insert some function>. Find the speed after X seconds. my question is, how do you know if the function is referring to the position of the object, or the velocity, or...
  21. Arkavo

    Varying Potential Energy and Amplitude in Unusual Harmonic Motion

    Homework Statement The potential energy of a particle varies as U=K|X|3, it is oscillating and the amplitude is 'A' then find out the time period's variance with 'A' Homework Equations F=-dU/dx a=F/m The Attempt at a Solution none..
  22. W

    Simple Harmonic Motion in an Elevator

    Homework Statement A simple pendulum is 5m long. What is the period of the oscillations for this pendulum in an elevator accelerating upwards at 5m/s2 and accelerating downards at 5m/s2Homework Equations ω = √(g/L) T = 2∏ / ωThe Attempt at a Solution I got the right answers (trial and...
  23. F

    Is this simple harmonic motion?

    Homework Statement The displacement of a particle along x-axis given by x=A sin^2(wt), where the symbols have their usual meaning. Is the particle motion simple harmonic? also find its time period. Homework Equations simple harmonic eqn iss of the form x=Asin(wt) or x=acos(wt)...
  24. S

    Energy calculation in Simple harmonic motion

    Hello why we use cosine and sine in simple harmonic motion? why we use particularly cosine with potential energy and sine with kinetic energy of simple harmonic oscillator? regards
  25. N

    Simple Harmonic Motion on a Uniform Meter Stick

    Homework Statement A uniform meter stick of mass M is pivoted on a hinge at one end and held horizontal by a spring with spring constant k attached at the other end. If the stick oscillates up and down slightly, what is its frequency? Homework Equations τ=rFsinθ f=(1/2π)√(k/m) F=kx...
  26. S

    Simple harmonic motion of a spring and mass

    Homework Statement A mass hanging from a spring is displaced and released so that it vibrates vertically. Its maximum height above a tabletop is 30 cm and its minimum height above the table top is 12 cm. The mass vibrates 20 times per minute. At time 0, its height is 30 cm...
  27. J

    Question about this simple harmonic motion problem

    Homework Statement A particle with a mass of 65 g is moving with simple harmonic motion. At time t = 0, the particle is at its extreme positive displacement of 18.0 cm. The period of the motion is 0.600 s. Find the vecocity of the particle at t = 1.35 s Homework Equations (1). ω=2∏/T...
  28. sankalpmittal

    Question- Angular Simple Harmonic motion

    Question--- Angular Simple Harmonic motion.. Homework Statement A spherical ball of mass "m" and radius "r" rolls without slipping on a rough concave surface of large radius "R". It makes small oscillations about the lowest point. Find the time period of such oscillations. Homework...
  29. J

    Find Amplitude and Equilibrium in Simple Harmonic Motion

    Homework Statement A 0.241-kg particle undergoes simple harmonic motion along the horizontal x-axis between the points x1 = -0.349 m and x2 = 0.419 m. The period of oscillation is 0.511 s. Find the frequency, f, the equilibrium position, xeq, the amplitude, A. Homework Equations The...
  30. Y

    Periodic Motion and Simple Harmonic Motion Terminology Question

    In lecture, we are beginning to learn about waves and periodic motion under simple harmonic motion. We were given the equations: x=Acosθ and θ=ωt+\phi -- Substituting, we get x=Acos(ωt+\phi). This is simple enough; however what is Phi? All I was told is that "phi is a constant that allows us...
  31. H

    Simple Harmonic motion : Is energy conserved

    Homework Statement I doubt energy is conserved in SHM, or it might be possible that i be doing something wrong. The particle (red dot) in the attachment is at its equilibrium position and oscillates with Simple Harmonic Motion between the two yellow colored plates. Amplitude A = 1.5 m...
  32. E

    Damped Simple Harmonic Motion - Finding drag constant

    Homework Statement Part (iv) The Attempt at a Solution My attempt is below. Is it correct ? Homework Statement
  33. P

    Simple Harmonic Motion (F=-kx) - Help

    Simple Harmonic Motion (F=-kx) -- Help! Hello Ladies & Gentlemen please answer my question: Q: The formula for Hooke's LAW is Felastic=-kx , so, the "X" is always negative? And the "F" is always negative? I know the "K" is always should be positive but please explain to me because I'm confused...
  34. A

    Finding acceleration, velocity, and time for simple harmonic motion

    Homework Statement A cheerleader waves her pom-pom in simple harmonic motion with an amplitude of .180m and a frequency of .850Hz. a) Find the maximum magnitude of the acceleration and of the velocity. b) Find the acceleration and speed when the pom-pom's coordinate is x=+.090m. c)...
  35. E

    Damped Harmonic Motion - Oscillating Spring

    Homework Statement http://www.mediafire.com/view/?7045cz9au1ci7cd A mountain bike has bad shock absorbers (w0/γ = 10) that oscillate with a period of 0.5 seconds after hitting a bump. If the mass of the bike and rider is 80kg, determine the value of the spring constant k (remembering that...
  36. E

    Understanding Damped Harmonic Motion

    So my professor was discussing the case of a mass suspended from a vertical massless spring in some viscous liquid. He arrives at the equation of motion which was :x: + \frac{b}{m}x. + \frac{k}{m}x = 0 x: is the second derivative of displacement wrt time. similarly x. is the first derivative...
  37. C

    How to solve 2nd order diff. equation for simple harmonic motion

    In my physics class we're talking about LC and LRC circuits, and the equations are analogous to those for SHM. However, I don't see how x=Acos(ωt+\varphi) satisfies m(d^2x/dt^2)+(k/m)x=0. I've never done differential equations and in the book it seemed like the author just guessed and checked...
  38. H

    Approximating a Simple Harmonic motion

    Homework Statement Homework Equations F=ma The Attempt at a Solution I did the first three parts . The last part of this question is quite hard, i tried using Newton's 2nd law of motion but ... here is what happens : T is the tension, as stated in the question . so the equation of...
  39. X

    Simple Harmonic motion and Doppler effect question

    Homework Statement So you're being pushed on a swing by someone who is whistling at a constant 60Hz. At the bottom, Vmax is 4 m/s. Explain what you hear as you swing toward and away from the source of whistling (speed of sound is 343 m/s for this problem). Homework Equations Observed...
  40. J

    Which equation to use in a Simple Harmonic Motion

    Im kind of confused on which acceleration equation to use. A = -(kx)/m or A = -(w^2)Acos[(angular freq)(time) + phase constant] as both of these contribute to SHM. Im guessing I can use the first acceleration equation when i know how far the object stretched and if i don't i...
  41. A

    Simple harmonic motion energy conservation problem

    Homework Statement A mass m hanging on a spring oscillates vertically. If the equilibrium point of the oscillation is a distance d below the relaxed length of the spring and if the amplitude of the oscillation is A, what is the maximum kinetic energy of the oscillation?[b]2. Homework Equations...
  42. L

    Undamped Harmonic Motion (ODE problem)

    Homework Statement A 24-lb weight, attached to the end of a spring, stretches it 4 inches. Find the equation of motion if the weight is released from rest from a point 3 inches above the equilibrium position. Homework Equations \frac{d^{2}{x}}{dt^2}+\frac{k}{m}x=0 F=ma The Attempt...
  43. Hardik Batra

    Simple Harmonic Motion: Limitations of T

    what is the limitation of T = 2π \sqrt{\frac{m}{k}}
  44. W

    Particle in Simple Harmonic Motion

    Homework Statement Not exactly sure why a time value of 0.500s is given, but I am positive it is why my answer isn't correct: Q. a 1kg object is attached to a horizontal spring. The spring is initially stretched by 0.100m and the object is released from rest there. It proceeds to move...
  45. C

    How Do You Calculate the Time Period of SHM for a Liquid in a U-Shaped Tube?

    Homework Statement We have U-shaped tube filled with liquid , if liquid is displaced through length 'x' find time period of SHM please help me :confused:
  46. B

    Simple Harmonic Motion: Mass on a Spring Homework Solution

    Homework Statement A massless spring hangs down from a support, with its lower end at y=0, where the y-axis is vertical and points downward (normal orientation of y). When a small unknown mass is attached to the spring, the lower end of the spring moves down to a position y_0 for the mass...
  47. H

    Initial displacement in Simple Harmonic Motion

    Homework Statement A meterstick is clamped to a tabletop. The end of the meter stick is deflected downwards a small distance x and is released such the end of the meterstick moves up and down in simple harmonic motion. The meterstick is measured to oscillate up and down 10 times in 5.0...
  48. W

    Question on Simple Harmonic Motion.

    Homework Statement A 100g particle hangs freely at rest on the end of a spring of stiffness 10N/m. If the particle is projected upwards with a speed of 2m/s, find the time taken until it first comes to rest and the distance travelled. Homework Equations Well, there's F = -k.x and of course the...
  49. I

    How can Simple Harmonic Motion have angular frequency?

    It isn't making any intuitive sense. If it isn't moving in circular motion, how can it have angular frequency or speed? Also, v=\pm ω\sqrt { A^{ 2 }-x^{ 2 } } only applies to SHM with springs only, right? Also, does anyone know how to derive this equation below? x=\frac { \pm \sqrt { { { v...
  50. PhizKid

    Simple harmonic motion on an incline

    Homework Statement Homework Equations F = -dU/dx The Attempt at a Solution U = \frac{1}{2}kx^2 + mgxsin\theta \\\\ F = -(kx + mgsin\theta) \\\\ F = -kx - mgsin\theta \\\\ We want to set the force = 0 because that's when the block is in equilibrium with no forces acting on...
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