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. thebosonbreaker

    Simple Harmonic Motion: why sin(wt) instead of sin(t)?

    Hello, I have recently been introduced to the topic of simple harmonic motion for the first time (I'm currently an A-level physics student). I feel that I have understood the fundamental ideas behind SHM very well. However, I have one question which has been bugging me and I can't seem to find a...
  2. Jozefina Gramatikova

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    Homework Statement Homework Equations [/B]The Attempt at a Solution I can solve everything but d). Please help
  3. Zubair Ahmad

    Simple Harmonic Motion: What is Superposition of SHM?

    What does superposition of SHM means physically.. I mean how is it that two shms superpose on same system?
  4. A

    Simple harmonic motion of charged particles

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  5. Jozefina Gramatikova

    Understanding Simple Harmonic Motion: Explaining x=Acos(wt+phi)

    Homework Statement x=Acos(wt+phi) Homework Equations can somebody explain to me please when phi=0. I saw many different questions with many solutions and I can't understand when we have just x=Acos(wt) and when x=Acos(wt+phi) The Attempt at a Solution
  6. J

    Simple Harmonic Motion - rearranging equation

    Homework Statement How to rearrange following equation? Homework Equations f = (1/2pi) square root of (k/m) The Attempt at a Solution (f^2 x m)/ (1/2pi)^2 Is this how i would do it?
  7. J

    Simple Harmonic Motion - Speed

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  8. G

    The phase of a simple harmonic motion

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  9. lc99

    Simple Harmonic Motion with Linear Momentum

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  10. F

    Is the Total Force in Damped Harmonic Motion Always Opposite to Velocity?

    Homework Statement Reading chapter 4 of Morin's "Introduction to classical mechanics" I came across to the explanation of the damped harmonic motion. The mass m is subject to a drag force proportional to its velocity, ##F_f = -bv ##. He says that the total force of the mass is ##F= -b \dot{x}...
  11. A

    What amplitude of simple harmonic motion of the spring....

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  12. F

    Harmonic Motion of a Charged Particle

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  13. L

    Simple Harmonic Motion of Meterstick

    Homework Statement Homework Equations ##\tau = rFsin(\theta)## ##\tau_{net} = I\alpha## ##F = -kx## ##kx = mg## The Attempt at a Solution I don't understand how the restoring force from the bending of the ruler behaves (so I have no idea how to apply torque here). I also don't understand how...
  14. Hydrous Caperilla

    How Is Simple Harmonic motion possible here?

    One thing I don't understand is that How Amplitude is conserved on both sides if the mass is subjected to different forces on either side of this shm...
  15. Y

    Solve a system of two linked harmonic oscillators

    $$m_1 \ddot{x} - m_1 g + \frac{k(d-l)}{d}x=0$$ $$m_2 \ddot{y} - m_2 \omega^2 y + \frac{k(d-l)}{d}y=0$$ It is two masses connected by a spring. ##d=\sqrt{x^2 + y^2}## and ##l## is the length of the relaxed spring (a constant). What is the strategy to solve such a system? I tried substituting...
  16. Y

    Simple Harmonic Motion in x direction

    Homework Statement A simple harmonic oscillator, with oscillations in the x direction, has velocity given by: $$v_{x} = (2.2 \frac {\mathrm{m}} {\mathrm{s}}) \sin [(6.9 \frac {\mathrm{rad}} {\mathrm{s}}) t]$$. Find the values of ##\omega , A, f , T ,## and ##\phi## Homework Equations $$v_{x} =...
  17. L

    Marble rolling on ramp harmonic motion

    Homework Statement A perfectly solid marble of radius R rolls without slipping at the bottom of a spherical bowl of a radius 6R. The marble rolls back and forth in the vertical plane executing simple harmonic motion close to the lowest point. How long does it take the marble to go down one side...
  18. william

    Harmonic motion of loudspeaker

    Homework Statement the cone of a loudspeaker vibrates in SHM at frequecy of 262Hz. the amplitude at the center of the cone is A=1.5X10^-4m and t=0 and x=A (amplitude). 1) what equation describes the motion of the center of the cone ? 2) what are the velocity and acceleration as a function of...
  19. J

    Simple harmonic motion springs

    I have a spring with mass M attached, and leave it at equilibrium. Then I displace it some more by stretching it down a bit more. Displacement due to the mass= X, displacement due to stretching it even more=Y. Why isn't the amplitude of oscillation= X+Y, but is only actually only Y? This is...
  20. A

    Angular Velocity in Simple Harmonic Motion

    I am very confused about angular velocity ω and why its used in simple harmonic motion. ω is described as θ/τ but when it comes to masses on springs, there is no angle - it is zero. Angular velocity comes from circular motion but the motion of SHM is not circular. My confusion is even greater...
  21. A

    Simple Harmonic Motion question (Need clarification)

    Homework Statement The point of the needle of a sewing machine moves in SHM along the x-axis with a frequency of 2.5 Hz. At t=0 its position and velocity components are +1.1 cm and -15 cm/s, respectively. (a) Find the acceleration component of the needle at t=0 (b) write an equation giving the...
  22. J

    Calculating Amplitude and Acceleration in Harmonic Motion - Physics Homework

    Homework Statement A spring holds a weight of 800 g. The spring is set in a harmonious swing. The frequency f for the oscillation is 1.4 Hz. When the weight is 5 cm above the equilibrium position on the way upwards, a velocity of 1.1 m / s is noted a) Determine the amplitude of the movement. b)...
  23. C

    Understanding Simple Harmonic Motion: Equations and Solution Attempt

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  24. N

    Simple Harmonic Motion: conceptual idea of angular frequency

    One of the conditions to distinguish Simple Harmonic Motion from other harmonic motions is by the relation that a∝x where x is the displacement from the point that acceleration is directed towards But what confuses me is the constant of proportionality introduced to this relation: ω2 ω is...
  25. J

    Finding Parameters for Simple Harmonic Motion at t=1

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  26. A

    Simple harmonic motion -- The spring and mass are immersed in a fluid....

    1. A mass, M = 1.61 kg, is attached to a wall by a spring with k = 559 N/m. The mass slides on a frictionless floor. The spring and mass are immersed in a fluid with a damping constant of 6.33 kg/s. A horizontal force, F(t) = Fd cos (ωdt), where Fd = 52.5 N, is applied to the mass through a...
  27. E

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  28. Feodalherren

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  29. Rotnort

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    Homework Statement I do not fully grasp the concept behind all of these sub questions (i)-(iv). Homework Equations v=wAcos(wt) (SMH)? Friction Force = Coefficient of Friction * Normal Force The Attempt at a Solution (i) Varying as simple harmonic motion sees varying acceleration as it...
  30. Mateus Buarque

    Simple Harmonic Motion and equilibrium of springs

    The figure below shows a system in equillibrium. The pulley and the springs (both with constants "k") are ideal. The period of oscillation of the mass A is given by: Relevant equations: F = -kx (SHM) I tried to do a "force diagram" and set up some geometric relations but it´s not working.
  31. ciao_potter

    Acceleration in Harmonic Motion

    Problem: A pendulum that has a period of 3.00000s and that is located where the accleration due to gravity is 9.79 m/s^2 is moved to a location where the acceleration due to gravity is 9.82 m/s^2. What is its new period, in s? Equations Equation for Harmonic motion: x = A sin (2pi * f * t)...
  32. EthanVandals

    Simple Harmonic Motion of a Spring?

    Homework Statement If a mass attached to a spring has motion given by the equation X(t) = 5(sin(3pi(t))), what is the equation for the acceleration of the spring? What is the angular speed of the spring,and what is its frequency and period? If the spring has a spring constant of 900 N/m, what...
  33. E

    Simple harmonic motion in an accelerating car

    There's a pendulum attached to a car accelerating with ##A##. I know I can find it's time period using the "effective" g method, but I want to find it from first principles. My attempt: ##tan\theta = A/g## Now I displace it by ##\alpha## giving ##mgsin(\theta+\alpha)-mAcos(\theta+\alpha) = ma##...
  34. F

    Finding the Value of Theta in Simple Harmonic Motion - Explanation and Solution

    Homework Statement The question is uploaded. The Attempt at a Solution I have completed the whole question, however, stuck on the last part. How to find the value about which ## \rm \small \theta## now oscillates? A source stated that ## \rm \small \alpha## is the value about which ## \rm...
  35. patrickmoloney

    Finding the Zeros of Damped Harmonic Motion Equations

    Homework Statement Solve the damped harmonic motion system \ddot{x} + 2k\dot{x} + \omega^2 x = 0 with initial conditions \dot{x}=V at x = 0 in the cases (i) \, \omega^2 = 10k^2 (ii) \omega^2 = k^2 (iii) \omega^2 = 5, k = 3 Identify the type of damping, sketch the curve of x versus t>0 in...
  36. John Doe

    I Amplitude of particles in the medium of a longitudinal wave

    I was thaught you can create a sinusoidal wave by making a source oscillate with simple harmonic motion in a medium, such as moving one end of a rope up and down to create a periodic transverse wave. For transverse waves, it is easy to see that every particle in the rope moves up and down with...
  37. R

    Simple harmonic motion displacement equation confusion

    Okay, so I have just started with simple harmonic motion(SHM). So the equation of displacement in my textbook is given as: X= ACos(wt +x) where A is the amplitude X is displacememt from mean position at time t w is angular frequency x is phase constant...
  38. K_Physics

    Standing Waves On Strings: Harmonic and Frequency Problem

    Homework Statement String A is stretched between two clamps separated by distance L. String B, with the same linear density and under the same tension as string A. String B is stretched between two clamps separated by distance 4L. Consider the first eight harmonics of string B. For which of...
  39. harini07

    A problem Simple harmonic motion

    Homework Statement A particle of mass 10g is placed in potential field given by V= (50x^2+100)erg/g. what will be the frequency of oscillation? Homework Equations n(frequency)=2pi(K/m)^1/2 The Attempt at a Solution F= -dU/dx . given is potential field. so dU/dx= (2*50x +0)=-100x. equating it...
  40. anon11

    Ball on a Turntable Simple Harmonic Motion

    Homework Statement A spherical ball of mass “m”, moment of inertia “I” about any axis through its center, and radius “a”, rolls without slipping and without dissipation on a horizontal turntable (of radius “r”) describe the balls motion in terms of (x,y) for a function of time. **The...
  41. L

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    Homework Statement http://imgur.com/a/FDfAp What is the phase constant? Homework Equations x(t) = A*cos(ωt+Φ) The Attempt at a Solution If I'm not mistaken at t = 0 the graph starts at half the amplitude or 5. Also the amplitude of this graph is 10, and at t = 0 angular velocity is also 0. 5...
  42. K

    Simple Harmonic Motion - Determine the period of oscillation

    Homework Statement A very light, rigid rod with a length of 0.620m extends straight out from one end of a meter stick. The stick is suspended from a pivot at the far end of the rod and is set into oscillation. (a)Determine the period of oscillation. (b)By what percentage does this differ from...
  43. R

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    Homework Statement you are taking your pendulum clock with you to a visit of the Jupiter moon Io(radious 3643.2Km, mass 8.94X10^22 kg. calculate the duration of a full Oscillation. On the surface this oscillation time was 1s Homework Equations T=2*π√l/g[/B]The Attempt at a Solution T1/T2=√(g2/g1)
  44. K

    Simple Harmonic Motion & Centripetal Force

    If there is a length thread with a metal ball attached at the end of the thread, and there is a oscilliation. The restoring force is F=mgsinθ, my question is can we consider this as a centripetal force and link it to this equation: mv^2/r.
  45. Vanessa Avila

    Simple Harmonic Motion Given Amplitude and Frequency

    Homework Statement A cheerleader waves her pom-pom in SHM with an amplitude of 17.3 cm and a frequency of 0.830 Hz . Find the maximum magnitude of the velocity.Homework Equations v = -w Asin(ωt+Φ) = -wx or Conservation of Energy: 1/2kx2 + 1/2mv2 = 1/2kA2 The Attempt at a Solution I tried v =...
  46. Vanessa Avila

    Simple Harmonic Motion: Finding displacement at given time t

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  47. P

    Solving Harmonic Motion: Find Equilibrium Points & Frequency

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  48. S

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  49. Wes Ellgass

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  50. W

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