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. E

    Simple harmonic motion question

    Homework Statement An object undergoing SHM with a period 0.9s and amplitude of 0.32 m at t=0 the object is at 0.32 m and is instantaneously at rest. Calculate the time it takes the object to go a) from 0.32 to 0.16 m b) from 0.16 m to 0 i can do a but don't understand why when i do the...
  2. D

    Simple Harmonic Motion - Mass and massive spring

    Homework Statement A block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a horizontal, frictionless track (Figure P15.62). The force constant of the spring is k and the equilibrium length is l. Assume that all portions of the spring oscillate in...
  3. D

    Simple Harmonic Motion with Cylinder Attached to Spring

    Homework Statement Okay, so we've got a solid cylinder attached to a horizontal massless spring that rolls without slipping along a horizontal surface. The system is released from rest with the spring stretched past the equilibrium point. (The first two parts of this problem ask for...
  4. 0

    Simple Harmonic Motion Problems

    I am having a hard time solving for k in the equation T = 2 x pi sq. rt. (m/k) I know this is simple algebra but its keeping me from solving this.
  5. T

    Energy and Simple Harmonic Motion of spring

    Homework Statement A 2.00-kg object is hanging from the end of a vertical spring. The spring constant is 50.0 N/m. The object is pulled 0.200m downward and released from rest. Complete the table below by calculating the translational kinetic energy, the gravitational potential energy, the...
  6. B

    Ball on String, Harmonic Motion

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  7. A

    What is the connection between simple harmonic motion and pendulum motion?

    Homework Statement What is the connection between simple harmonic motion and pendulum motion? Homework Equations Harmonic motion period=T=2piroot(m/k) Pendulum motion period=T=2piroot(L/g) The Attempt at a Solution Conservation of momentum?? Thanks for any help!
  8. N

    Pendulum/Simple Harmonic Motion, what is its energy of motion?

    A 1.2 kg mass attached to a spring oscillates with an amplitude of 5.1 cm and a frequency of 2.1 Hz. What is its energy of motion? I just have to use KE=1/2mv^2 right? do I have to involve the amplitude?
  9. J

    Simple harmonic motion of some mass

    Homework Statement A 0.25-kg mass is attached to the end of a spring that is attached horizontally to a wall. When the mass is displaced 8.5 cm and then released, it undergoes SHM. The force constant of the spring is 1.4 3 102 N/m. The amplitude remains constant. (a) How far does the mass...
  10. W

    Simple harmonic motion of a pendulum

    Homework Statement I need to find the phase difference between two pendulums. My problem is that I don;t seem to have enough information to calculate the phase for the second pendulum (I have already calculated the phase for the first). The pendulum is 0.35m long, and is at 0.00rad at...
  11. Z

    Simple Harmonic Motion

    There is a horizontal spring-mass system lie on top of a frictionless table. let m=mass k=spring constant x=displacement from equilibrium position A=amplitude T=period By using conventional way, time taken to complete a quarter of cycle=T/4=(∏/2)√(m/k) consider another way of doing...
  12. S

    Instances of simple harmonic motion?

    Hi, I have this simple harmonic motion lab, it can't be a simple pendulum lab where you manipulate mass or length of string, it can't be a spring with hanging weight either, I really have no idea what to do, is there any other way to demonstrate simple harmonic motion? thanks.
  13. R

    Simple Harmonic Motion and vibration

    Homework Statement A mass of 0.3kg is suspended from a spring of stiffness 200Nm-1. If the mass is displaced by 10mm from its equilibrium position and released, for resulting vibration, calculate: a) the maximum velocity of the mass during the vibration Homework Equations Angular...
  14. A

    * *Damped Harmonic Motion (Differential Equations)

    *URGENT*Damped Harmonic Motion (Differential Equations) A damped harmonic oscillator satisfies the following equation: d2x/dt2 = − 5x − 2dx/dt (a) By assuming a trial function of the form x = A e^qt, determine the solution of this equation "from scratch." Express your final answer as a real...
  15. H

    Simple Harmonic Motion of spring

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  16. J

    Conceptual question on Simple Harmonic Motion.

    Homework Statement Given that a spring with a ball of mass m attached to it is oscillating in between x=A and x=-A where x=0 is the equilibrium position. Will the equilibrium position change when the the mass of the ball is doubled? 2. The attempt at a solution I think that the...
  17. R

    Simple Harmonic Motion vibration Question

    Homework Statement A mass of 0.3kg is suspended from a spring of stiffness 200Nm-1. If the mass is displaced by 10mm from its equilibrium position and released, for resulting vibration, calculate: a) the frequency of vibration b) the maximum velocity of the mass during the vibration c) the...
  18. F

    Classical Mechanics, Coupled Harmonic motion

    Homework Statement Set up the equations of motion for the system shown in Fig. 4.16. The relaxed lengths of the two springs are l1, l2 . Separate the problem into two problems, one involving the motion of the center of mass, and the other involving the "internal motion" described by the two...
  19. QuarkCharmer

    Simple Harmonic Motion of a bolt of mass

    Homework Statement A bolt of mass 2.10×10^-2 kg moves with SHM that has an amplitude of 0.245 m and a period of 1.495 s. The displacement of the bolt is + 0.245 m when t=0. A.) Find the displacement of the bolt at time t=0.500s Homework Equations The Attempt at a Solution Part...
  20. P

    Calculating ∅ in Simple Harmonic Motion Equation x = xo + Asin(ωt + ∅)

    x = xo + Asin(ωt + ∅) I know all of the values, except for ∅. But i don't know how to get the value for ∅ The attempt at a solution: 0.349 = 0.367 + 0.413Sin(8.5 * 0.8938 + ∅) -0.018 = 0.413Sin(7.5973 + ∅) -0.04358 = Sin(7.5973 + ∅) From here on, i am confused, I tried using the...
  21. C

    Harmonic motion of a bungee jumper

    Homework Statement A bungee jumper undergoes simple harmonic motion with amplitude 6.9 m and frequency 0.115 Hz. Assume the bungee jumper follows the simple harmonic motion equation x=A\cos (\omega t). Find the velocity of the jumper at 0.25s Homework Equations x=Acos(\omega*t)...
  22. J

    Simple Harmonic motion of buoyant force

    Homework Statement a cylinder is in a deep pool of liquid. it has mass 2kg, diameter 10cm, height 15cm. the density of the liquid is 1.5g/cm^3. The cylinder is submerged up to 12cm, and let go. Show that the resulting motion is simple harmonic. Homework Equations x=Acos(wt)...
  23. K

    Simple harmonic motion of a spring mass

    Homework Statement A spring of negligible mass have an original length of 1m. A load of 2kg is later added to it, resulting in an extension of 0.1m. Then it is pulled 0.02m and released. What is the amplitude of the simple harmonic motion. erm basically I just want to know which is the...
  24. H

    How to approach a simple harmonic motion problem

    This is the question: A massless spring with a spring constant of 0.50 N/m, has a mass of 0.7 kg on its end. The maximum speed of the end is 2.5 m/s. What is the angular frequency of the system? I don't know how to approach this problem at all. I just know that omega/2pi is the...
  25. L

    Understanding the Effect of Perpendicular Components in Simple Harmonic Motion

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  26. K

    Homework help: Harmonic Motion of a Spring and Block System

    Homework Statement Part 1: A 0.1 kg block attached to a spring of force constant 17.2 N/m oscillates with an amplitude of 16 cm. Find the the maximum speed of the block. I solved this part using the equations for angular frequency and max velocity. Part 2: Find speed of the...
  27. F

    Simple Harmonic Motion ) Vertical Spring

    Homework Statement A spring with spring constant 150 N/m hangs from a ceiling. A 2.00 kg mass is attached to the end of the spring and released. a) How far below its unstretched position will the mass be in equilibrium? b) How far below its unstretched position will the mass fall? c) Taking...
  28. J

    Simple Harmonic Motion Phase angle

    Homework Statement What is the initial phase angle of this graph that describes a simple harmonic motion? Homework Equations The Attempt at a Solution I don't have any clue about how to find it by watching the graph, I know only an equation to find it. Any help please.
  29. J

    Finding Period and Angular Frequency in Simple Harmonic Motion

    Homework Statement a particle moves to the right along the x-axis with a simple harmonic motion from x0 = 3.0cm in t=0 . if its position x is given by x = 4.0 cos (pi t + phi) , in cms ; find its period T. Homework Equations The Attempt at a Solution The problem ask me more...
  30. P

    Simple Harmonic Motion - Acceleration and Time Period

    Hi, I am a bit confused regarding the relation between the acceleration and time period in simple harmonic motion. This questions asks what would be one change to the motion of a car's wing mirror in case the glass was switched for a heavier one. I don't understand for example, how would...
  31. P

    Simple Harmonic Motion mass homework

    Hi, I am not very good with questions that ask me to asses a scenario qualitatively in SHM... So, if you guys can maybe guide/advise me how to go about these here: 1.A body is suspended vertically at the end of a spring that is attached to the ceiling of an elevator. The elevator moves...
  32. P

    Simple Harmonic Motion - Acceleration and Velocity

    Hi, 9 (a) Write down an equation for the displacement of a particle undergoing SHM with an amplitude equal to 8.0 cm and a frequency of 14 Hz, assuming that at t = 0 displacement is = to 8.0 cm and the particle is at rest. What I got (and this agrees with the book) was: x = 8.0 cos...
  33. S

    Harmonic Motion of a Ball in a Hole at Earth's Centre

    suppose if we make hole at the centre of Earth and release a ball into it,then it exhibits simple harmonic motion about the centre,please explain
  34. S

    Rolling a half full water bottle and simple harmonic motion

    hi I am just saw this phenomenon and see if there is any links to the topic that I am learning in school. So when i rolled a half full (depends on how optimistic you are :smile:) water bottle with a certain amount of force, the bottle went back and forth for a little while before stopping...
  35. M

    Simple Harmonic Motion: Acceleration Max/Min

    Hi, i need some help for a physics question: when is acceleration at maximum and when is acceleration at minimum in a simple harmonic motion. i know when the speed is at maximum: at the equilibrium position; however, i do not know about the acceleration. Please note that direction does not matter
  36. P

    Simple Harmonic Motion - Acceleration

    Hi, :smile: Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of oscillation, f, is given by the expression: f = 1 / 2π * √(k/m) where k is the force per unit displacement between a hydrogen atom and the carbon atom and the m is the mass of a proton. (i)...
  37. A

    Simple Harmonic Motion and frequency

    Homework Statement A mass sits on a platform undergoing simple harmonic motion in the vertical direction. The mass loses contact with the platform when the amplitude exceeds 6.2 cm. What is the frequency, f (in Hz), of the platform’s vibration? Take g = 9.8ms−2. Homework Equations...
  38. A

    Simple harmonic motion and particle speed

    Motion of particle shows a max acc. of 30 m/s2 and a frequency of 120 cycles per minuet. assuming SHM determine, the amplitude and max velocity. i found the sqrt of k/m to be 12.57 even though neither was given and the frequency to 2 cycles/sec. i do not know what relations to use to work...
  39. N

    Amplitude of a simple harmonic motion equation

    if you have the equation: x(t) = Acos(ωt + ϕ) and you have the following information: A 200 g block hangs from a spring with spring constant 10 N/m. At t = 0s the block is 20 cm below the equilibrium position and moving upward with a speed of 100 cm/s. The answers give a short method of...
  40. A

    Simple harmonic motion in a string

    Homework Statement Hi I need some clarification on this question A light elastic string of natural length 50 cm and modulus 20 N has one end fastened to O on a smooth horizontal table. The other end has a particle of mass 0.4 kg attached to it and the particle is released from rest at a...
  41. A

    Sound Waves (simple harmonic motion and pressure dilemma)

    I've encountered a bit of a conceptual problem in my studies and I was hoping someone could help me out with this: I understand that the longitudinal sound wave takes the form of the equation s(x,t) = smcos(kx +/- wt), and that the equation for pressure variance produced by the sound wave...
  42. K

    Simple Harmonic Motion , finding the time taken to travel an angular dispalcemnt

    1. Homework Statement Find the time taken to reach half the maximum angular displacement in a PENDULUM. Given that the bob hanging at rest was given an initial velocity of 2ms, and the length of the string is 6m. 2. Homework Equations finding the angular velocity using sqrt.(g/l)...
  43. X

    How Does Simple Harmonic Motion Influence Precision Timing Devices?

    1. Two people build precison timing devices, one with a simple pendulum, one with a simple mass-spring. Each is to have a period of 2 s. The Fg = 9.8 m/s^2. Select the appropriate parameters for this to happen. Part B - which device is more precise at the equator? 2. I have no idea :(...
  44. D

    Displacement Meter- Simple Harmonic Motion

    Homework Statement The figure attached shows the meter used to study the motion yB = bsinωt. The motion of the mass relative to the frame is recorded on the drum. If l1= 360 mm, l2= 480 mm, l3= 600 mm, m = 0.9 kg, c = 1.4 Ns/m and ω = 10 rad/s, Determine the range of the spring...
  45. S

    Simple Harmonic motion (non-calculus)

    Homework Statement Atoms in a solid are not stationary, but vibrate about their equilibrium positions. Typically, the frequency of vibration is about f = 2 E12 Hz and the amplitude is about 1.1 E-11m. For a typical atom, what is its (a) maximum speed? Homework Equations T= 1/f. v = change...
  46. J

    Evergy of Simple harmonic motion

    Homework Statement A 0.155 kg mass is attached to a spring and executes simple harmonic motion with a pe- riod of 0.63 s. The total energy of the system is 1.9 J. Find the force constant of the spring. Homework Equations E=1/2(kA^2) The Attempt at a Solution We went...
  47. G

    Simp,e Harmonic Motion with Damping

    Hey, I have a simple question to ask. Some sources I have seen develop the solution for the underdamped case with an exponential term multiplied by a Cosine term. This is due to the application of the Euler identity to the solution with two exponentials each with one of the complex conjugate...
  48. D

    Simple harmonic motion spring problem

    Homework Statement The drawing shows a top view of a frictionless horizontal surface, where there are two springs with particles of mass*m1*and*m2*attached to them. Each spring has a spring constant of*120*N/m. The particles are pulled to the right and then released from the positions shown in...
  49. C

    Simple Harmonic Motion of a 2kg particle

    Homework Statement A 2kg particle undergoes simple harmonic motion according to x=1.5sin((pi*t/4) + Pi/6) A)What is the total mechanical energy of the particle? B) Shortest time for particle to go from x=.5m to x=-.75m Homework Equations Potential energy=.5kx^2 The Attempt at a...
  50. I

    Simple Harmonic Motion and Static Friction. I am stumped.

    Homework Statement During an earthquake, a floor oscillates horizontally in approximately simple harmonic motion. Assume it oscillates at a single frequency with a period of 0.84 s. After the earthquake, you are in charge of examining the video of the floor motion and discover that a box on...
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