What is Simple harmonic motion: Definition and 913 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. Shivang kohlii

    Shm , calculation of amplitude of spring mass system

    Homework Statement In A spring mass system , the spring stretches 2 cm from its 's frelength when a force of 10 N is applied . This spring is stretched 10 cm from it's free length , when a body of mass m = 2 kg is attached to it and released from rest at time t = 0 . Find the A) force constant...
  2. Shivang kohlii

    Equation of shm for different positions

    Homework Statement Write the equation for a particle in simple harmonic motion with amplitude a and angular frequency w considering all distances from one extreme position and time when it is at other extreme end. Homework Equations X = A sin (wt + ∆) ∆ = phase difference The Attempt at a...
  3. Celso

    Simple harmonic motion interpretation problem

    I'm in trouble trying to understand the expression ##t= \frac{1}{\omega} cos^{-1}(x/A)## that comes from ##x = Acos(\omega t)##, in which ##A## is the amplitude, ##t## is time and ##x## is displacement. When ##x = 0##, ##t = \frac{\pi}{2\omega} ##, shouldn't it be 0 since there was no movement?
  4. T

    Simple harmonic motion equation

    Homework Statement Calculate the harmonic motion equation for the following case A=0.1m, t=0s x=0.05m, v(t=0)>0 a(t=0)= -0.8m/s^2 Homework Equations x(t)= +/-Acos/sin ( (2pi/T)/*t) The Attempt at a Solution [/B] A is given to be 0.1 so I simply place it into the equation. Now I have to...
  5. M

    Does amplitude depend on mass in SHM?

    Homework Statement Does amplitude of an oscillating spring with an attached block depend on the block's mass? Assuming the spring has spring constant 'k' and obeys Hooke's law. How would the amplitude of the oscillating spring system be affected if the mass of the block were...
  6. astroman707

    Derive the formula for the frequency of a spring

    Homework Statement Two masses m1 and m2 are joined by a spring of spring constant k. Show that the frequency of vibration of these masses along the line connecting them is ω = √[ k(m1 + m2) / (m1*m2) ] (Hint: Center of mass remains at rest.) Homework Equations f = w/2π w = √(k/m) F = -kx a = -...
  7. J

    Confused about a simple harmonic motion problem....

    Homework Statement A vertical block-spring system on Earth has a period of 6.0 s. What is the period of this same system on the moon where the acceleration due to gravity is roughly 1/6 that of earth? Homework Equations w = √(k/m) w = (2Pi)/T T = 2Pi*√(m/k)[/B] The Attempt at a Solution So...
  8. Dorian

    Position vs Time Graph: Simple Harmonic Motion

    Homework Statement [see attached photo] I seek specific help with (a) only. The answers to this question are provided in the back of the textbook, so I know the answers (I hope). Homework Equations ##x(t)=Acos(\omega t+\phi _{0}),## ##v_{x}(t)=-A\omega sin(\omega t+\phi...
  9. S

    Simple Harmonic Motion derivation

    Homework Statement Hookes Law gives: F = -kx. This is SHM. But I cannot see how to get to the sinusoidal expression from this. (In all the explanations, they cheat, and just introduce de novo Omega or Omega^2.) But how do you get to m. d2x/dt^2 = -x.(omega) ^2 Homework Equations F = -kx. m...
  10. M

    How to derive a formula for simple harmonic motion?

    Homework Statement You need to derive a formula for undamped pendulum simple harmonic motion; 1. Starting from the middle point 2. Starting from the extreme point Homework Equations The solutions are; 1. s = s0 sin(2 pi f t) 2. s = s0 cos(2 pi f t) The Attempt at a Solution I can derive the...
  11. Salman Ali

    Which of the options describes the phase constant for SHM?

    The only thing I know is that phase constant tells how much a signal is shifted along the x-axis. The answer of the question is both option a and b. I am not getting it!
  12. Y

    Phase angle and Phase in Simple harmonic motion

    I'm a teacher at a Senior High School in Indonesia. I have two Senior High School physics books (Indonesian book) written about simple harmonic motion formula: y = A sin θ = A sin (ωt + θ0) = A sin 2πφ = A sin 2π (t/T + θ0/2π) phase angle = θ = ωt + θ0 phase of wave = φ = t/T + θ0/2π But I...
  13. komarxian

    SHM: Planet Problem Homework Statement

    Homework Statement You are exploring a newly discovered planet. The radius of the planet is 7.20 * 107 m. You suspend a lead weight from the lower end of a light string that is 4.00 m long and has mass 0.0280 kg. You measure that it takes 0.0685 s for a transverse pulse to travel from the...
  14. B

    Simple Harmonic Oscillator with Boundary Conditions

    How would you solve for the Amplitude(A) and Phase Constant(ø) of a spring undergoing simple harmonic motion given the following boundary conditions: (x1,t1)=(0.01, 0) (x2,t2)=(0.04, 5) f=13Hz x values are given in relation to the equilibrium point. Equation of Motion for a spring undergoing...
  15. 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...
  16. Jozefina Gramatikova

    Simple harmonic motion - damping introduced

    Homework Statement Homework Equations [/B]The Attempt at a Solution I can solve everything but d). Please help
  17. 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?
  18. A

    Simple harmonic motion of charged particles

    Homework Statement Two identical particles, each having charge +q, are fixed in space and separated by a distance d. A third particle with charge -Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between the two...
  19. U

    How Does a Spring Impact the Angular Frequency of a Pendulum?

    Homework Statement A pendulum of mass ##m## and length ##L## is connected to a spring as shown in figure. If the bob is displaced slightly from its mean position and released, it performs simple harmonic motion. What is the angular frequency of the bob? Homework Equations Angular frequency for...
  20. 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
  21. Safder Aree

    Simple Pendulum undergoing harmonic oscillation

    Homework Statement Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much? Homework Equations $$F = -mgsin\theta $$ $$T = mgcos\theta $$ The Attempt at a Solution I'm mostly confused by what it means by time average. However from my...
  22. M

    A Damped Harmonic Oscillator - Gravity not constant.

    Hello, I have a question regarding Damped Harmonic Motion and I was wondering if anyone out there could help me out? Under normal conditions, gravity will not have an affect on a damped spring oscillator that goes up and down. Gravity will just change the offset, and the normal force equation...
  23. 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?
  24. J

    Simple Harmonic Motion - Speed

    Homework Statement Calculate the speed of the block in SHM as it moves through equilibrium position. k= 45.08248265 N/m m of block = 0.505kg T = 0.665s Homework Equations w= the square root of (k/m) ? The Attempt at a Solution w = the square root of (45.08248265/0.505) = 9.448398958 =...
  25. G

    The phase of a simple harmonic motion

    Homework Statement How can I calculate the initial phase in a simple harmonic motion if I only have the amplitude, frequency and angular velocity as data? Homework Equations The formula of the position, in fact they ask me to do the formula that allows to know the elongation depending on the...
  26. Suyash Singh

    Spring SHM Homework: Solving for Displacement of a Suspended Point Mass

    Homework Statement A point mass m= 20 kg, is suspended by a massless spring of constant 2000 N/m. The point mass is released when elongation in the spring is 15 cm. The equation of displacement of particle as function of time is : (Take g = 10 m/s2) Homework Equations A is amplitude w is...
  27. lc99

    Simple Harmonic Motion with Linear Momentum

    Homework Statement Homework Equations T = 2pi * sqrt(m/k) mv =m2v2 (LM)[/B]The Attempt at a Solution [/B] So T2 depends on the mass and not velocity. So i can find T2 = 2pi * sqrt([m/2]/k) For A2 , i know that the amplitude before any collision is 1/2m1v1^2 = 1/2kA1^2 so solving that, i...
  28. A

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

    Homework Statement Answer: Can someone explain the answer? I don't understand why it's necessary for that the moment when the force exerted on the smaller block is greatest is when it is on the verge of slipping. Could it not already have been slipped off or maybe even 3/4 way slipped off...
  29. 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...
  30. Hydrous Caperilla

    Finding the time period of this System

    Homework Statement To find the time period of this simple harmonic motion Homework Equations F= -kx The Attempt at a Solution To check Simple harmonic motion first ,I have to displace the mass by some distance which I take to be x in this case. Therefore the spring will be displaced by a...
  31. 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...
  32. 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} =...
  33. 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...
  34. bahtiyar

    Swing and angular displacement

    hi, we are a few non-native English speaker physics teacher and we wrote some questions for an assessment book but we can't be sure about this two similar question. a) are they accurate for rules of English, are we use correct terms is there a necessary change? b) are they accurate for rules of...
  35. A

    Elastic potential energy problem

    Homework Statement A 1.00kg mass and 2.00kg mass are set gently on a platform mounted on an ideal spring of force constant 40.0 N/m. The 2.00 kg mass is suddenly removed. How high above its starting position does the 1.00 kg mass reach? Related to it... An 87 g box is attached to a spring with...
  36. 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...
  37. 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...
  38. E

    SHM Energy Conservation in a Spring

    1. The problem statement, all variables, and given/known data Describe the energy conversions in a spring undergoing simple harmonic motion as it moves from the point of maximum compression to maximum stretch in a frictionless environment. Focus on points at which there will be maximum speed...
  39. A

    I Solving the differential equations involving SHM

    What is the most satisfactory explanation for guessing certain solutions to the differential equations encountered in damped & driven SHM?
  40. C

    Understanding Simple Harmonic Motion: Equations and Solution Attempt

    Homework Statement Homework EquationsThe Attempt at a Solution I know that when displacement is max, kinetic energy is 0 and when displacement is o, kinetic energy is max and I know is should always be above the axis because KE can't be negative But what about the amplitude and frequency...
  41. 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...
  42. T

    How do i get the frequency of undamped motion?

    Homework Statement The single wheel of an aircraft can undergo a max of 7500N at a vertical velocity of 8 m/s on landing. The vertical spring moves in SHM and has a stiffness of 600N/mm. The systems vertical damper has a damping coefficient of 38 x 10^3 Ns.m-1 Homework Equations F=Kx...
  43. J

    Finding Parameters for Simple Harmonic Motion at t=1

    Homework Statement Consider a Simple Harmonic Motion (SHM) for which, at time t = 1 s, the displacement is s=1 cm, the velocity is 2 cm s−1, and the acceleration is −3 cm s−2. Find the angular frequency, 4. amplitude, and phase constant for this motion. Homework Equations f=1/T...
  44. 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...
  45. E

    Phase Difference in Parallel SHM with Equal Amplitude and Frequency

    Homework Statement Two particles move parallel to the x-axis about the origin with the same amplitude and frequency. At a certain instant, they are found at a distance A/3 from the origin, on opposite sides of the origin, with their velocities in the same direction. Find the phase difference...
  46. Rotnort

    Magnitude of Frictional Force in Simple Harmonic Motion

    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...
  47. 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.
  48. K

    Simple Harmonic Motion/Period of a Physical Pendulum

    I'm studying the motion of a physical pendulum, could someone help me make the final step in figuring out how to find the period so I can make predictions before carrying out a practical? Basically I have a meter rule with holes drilled along the length and will be pivoting it at various points...
  49. 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...
  50. F

    Trouble finding the amplitude in a SHM problem

    Homework Statement a horizontal spring-mass is composed of a spring with constant 10.0 N/m and an 80.0 gram mass on the end of the spring. the surface supporting the mass is friction less. when the system is first observed, the spring is extended 1.30 cm and the velocity of the mass is 54.1...
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