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.

View More On Wikipedia.org
Recent contents Top users
  1. N

    Simple harmonic motion problem

    I translated it, so the notation may not be so great. You have a vertical spring with a spring constant of 16 N.m^-1, we attach to its lower end a body with a mass of 0,4 KG and form a system which oscillates on a straight line with length of 8cm, we assume that at the start of the time, the...
  2. L

    Simple harmonic motion - answer slightly off

    Homework Statement A 4.00kg block is suspended from a spring with k = 500N/m. A 50.0g bullet is fired into the block from directly below with a speed of 125m/s and becomes embedded in the block. a) Find the amplitude of the resulting SHM. b) What percentage of the original kinetic energy of...
  3. K

    Weights and pulleys in harmonic motion

    Homework Statement No friction. m3=5m, m2=12m, m1=3m Prove that the system's acceleration when it's released is a=0.2g. is it the max acceleration? Show that the equilibrium point is at x0=0.75L Show that the kinetic energy of the system is E=mgL Show that m2 will stop momentarily at...
  4. D

    Simple Harmonic Motion and phase constant

    A simple harmonic oscillator consists of a block of mass 45 g attached to a spring of spring constant 240 N/m, oscillating on a frictionless surface. If the block is displaced 3.5 cm from its equilibrium position and released so that its initial velocity is zero, what is the phase constant, φ ...
  5. M

    Simple Harmonic Motion of a 12kg mass

    A 12kg mass undergoes simple harmonic motion with an amplitude of 10cm. If the force constant for the spring is 320N/m: a) Calculate the total energy of the mass spring system. Et=½kA^2 =½(320N/m)(0.1m)^2 =1.6 Jb) Calculate the maximum speed of the mass. Et=½mv^2 + ½kx^2 1.6 J = ½(12kg)v^2...
  6. Q

    Harmonic motion and Electrical Fields

    Homework Statement Two positive charges +Q are affixed rigidly to the x-axis, one at x = +d and the other at x = -d. A third charge +q of mass m, which is constrained to move only along the x-axis, is displaced from the origin by a small distance s << d and then released from rest. (a) Show...
  7. E

    Difference between X and Amplitude (Simple Harmonic Motion)?

    V=Vo √1-(x^2/a^2) X is the distance of the spring's stretch, but how would you rearrange the equation if you are looking for Amplitude? They both use the same units (meters) as far as I am concerned. Help would be appreciated, thanks; I am still a beginner with Physics.
  8. Samurai44

    Simple harmonic motion energy question

    Homework Statement Can I get help in part (b) of this question ? Homework Equations KE=1/2 m v2 v= (2π f )√(A2 - x2) The Attempt at a Solution I substituted the second equation into first one, so i got KE= 1/2 m (2π f )2 (A2 - x2) but then couldn't complete
  9. L

    Angular Simple Harmonic Motion

    1. The balance spring of a watch is a hoop 1.2 cm in diameter, with a mass of 0.65 g. If the watch is running 45 seconds per day too fast, by what percentage should the rotational inertia of the hoop be changed? 2. Homework Equations : I = mR^2 Ia = -k(theta) x(t) = Xm Cos(wt + @) (just using @...
  10. L

    Simple Harmonic Motion Question (Springs)

    A 350-g mass is attached to a spring whose spring constant is 64 N/m. Its maximum acceleration is 5.3 m/s2. What is its maximum speed? So, i had a go at the question which basically required the knowledge that maximum acceleration occurs when displacement is maximum and maximum velocity occurs...
  11. Z

    How Does the Invariance Principle Apply to Limits in Engel's Problem?

    Homework Statement Hi Guys, This is the first exampe from Engel's problem solving book. After a long period of no math I am self studying. I do not know where my knowledge deficits lie, and was recommended this site for help. "E1. Starting with a point S (a, b) of the plane with 0 < b < a...
  12. O

    Find the amplitude of the resulting simple harmonic motions

    Homework Statement An 8.0 lb block is suspended from a spring with a force constant of 3.0 lb/ in. A bullet weighing 0.10 lb is fired into the block from below with a speed of 500 ft/sec and comes to rest in the block. a) Find the amplitude of the resulting simple harmonic motions b) What...
  13. Calpalned

    Understanding Simple Harmonic Motion: Homework Equations and Graph Analysis

    Homework Statement My textbook states that for simple harmonic motion, the sinusoidal graph of the x (displacement) as a function of time can be created using the "Equation of motion". Homework Equations The equation of motion ##A \cos (\omega t + \phi)## The Attempt at a Solution I know...
  14. T

    Simple Harmonic Motion with Damping and Driving

    Hello, I was asked by my professor today to graph the motion, as well as the energies, of a spring that undergoes driven and/or damped oscillation; however, I was unable to because I do not have a very good idea of how they work. Can someone explain to me, qualitatively, what it means to have a...
  15. SherlockIsReal

    Comparing SHM of Two Identical Masses on Springs

    Homework Statement Compare the simple harmonic motion of two identical masses oscillating up and down on springs with different spring constants. Homework Equations F = -kxThe Attempt at a Solution Okay, so I understand that the higher the spring constant, the harder it is to compress the...
  16. M

    Simple Harmonic Motion: Particle Speed and Acceleration Calculation

    Homework Statement A particle moves with simple harmonic motion in a straight line with amplitude 0.05 m and the period 12 s.Find (a) the maximum speed , (b) the maximum acceleration of the particle.Write down the values of the constants P and Q in the equation x/m = P sin [Q)(t/s)] Homework...
  17. Futurestar33

    Harmonic Motion in One dimension -- Question in equation derivation

    Homework Statement I am curious as to how the second line in the equation is equal to the third line in the equation. The book my class is using is Taylor and it just skips so many steps. What happens to the sign, I know this must relate to euler in some way I am just not sure how. Thank you...
  18. kate Co

    Simple Harmonic Motion Question?

    Homework Statement A 0.500Kg object is undergoing simple harmonic motion at the end of a horizontal spring with force constant k=300N/m. When the object is 0.012m from the equilibrium position, it is observed to have a speed of 0.300m/s. What is: a) The total energy of the object at any point...
  19. P

    Simple Harmonic Motion problem with spring mass system

    Homework Statement A 50g mass is attached to a spring and undergoes simple harmonic motion. It's maximum acceleration is 15m/s and maximum speed is 3.5m/s. Determine a)angular frequency, b) spring constant, c) amplitude. Homework Equations ω = √k/m X(t) = A*cos(ωt + ∅) The Attempt at a...
  20. T

    Vertical Simple Harmonic Motion

    Homework Statement Homework EquationsThe Attempt at a Solution Suppose mass of platform is ##M_1## and that of coin is ##M_2## . The normal force between them is N . EOM for platform (mass M1) = ##-kx+M_{1}g+N = M_{1}\ddot{x}## EOM for coin(mass M2) = ##M_{2}g-N = M_{1}\ddot{x}## This...
  21. J

    Simple Harmonic Motion and acceleration

    Hi, I have a few questions relating to the equation for maximum acceleration for SHM: amax = A (2 x pi x f)^2 where amax = max. acceleration, A = amplitude, f = frequency. How are these variables supposed to be interpreted when you relate them to each other. For example, is A inversely...
  22. A

    Simple Harmonic Motion, Initial Displacement vs Initial Cond

    Hi everybody, I'm writing an exploration on the mathematics of simple harmonic motion and I stumbled across something I fail to understand in one of my resources (http://tutorial.math.lamar.edu/Classes/DE/Vibrations.aspx). In the example the author uses toward the end of the resource, the...
  23. C

    Can x=8sin2t+6cos2t be proven as S.H.M. using a second derivative?

    Homework Statement Prove that: x=8sin2t+6cos2t is undergoing S.H.M. (Not too sure about how to prove for solution.) Homework Equations Solution for S.H.M. x=asin(nt+α) is \frac{d^{2}x}{dy^{2}}=-n^2xThe Attempt at a Solution...
  24. S

    Simple Harmonic Motion oscillation amplitude

    Homework Statement A mass on a spring has an angular oscillation frequency of 2.56 rad/s. The spring constant is 27.2 N/m, and the system's kinetic energy is 4.16 J when t = 1.56 s. What is the oscillation amplitude? Assume that the mass is at its equilibrium position when t = 0.a. 63.1 cm b...
  25. P

    Simple Harmonic Motion & Pendulum Problem

    Homework Statement What length must the pendulum be changed to in order to show the correct time? L=0.5m After 12hours the clock is behind by 30minutes. Homework Equations w=sqrt(g/L) w=2πf The Attempt at a Solution I thought if I set the frequency equal to 1Hz and solved for length it would...
  26. Y

    Phase space diagram for a spring in simple harmonic motion

    Homework Statement A mass m = 750 g is connected to a spring with spring constant k = 1.5 N/m. At t = 0 the mass is set into simple harmonic motion (no damping) with the initial conditions represented by the point P in the phase space diagram at the right. **(This phase space diagram has...
  27. E

    How Do You Calculate the Period of Oscillation in a Harmonic Potential?

    Homework Statement A harmonic potential is parameterised as: V(x)=\frac{k}{2}(x-x_{0})^2An object moves within this potential with a total energy E > 0. (i) Where are the two turning points of the motion xA and xB? (ii) Write down the equation of motion for the object, and use it to find...
  28. F

    Velocity vs time graph simple harmonic motion phase constant

    Homework Statement http://i.imgur.com/u8vUv5a.jpg Find the phase constant. Homework Equations x(t)=Acos(ωt + Φ) v(t)=-Aωsin(ωt + Φ) Vmax = ωA ω=2π/T The Attempt at a Solution ω = 2π/12 = 0.5236 A = 60/0.5236 = 114.59 cm v(0) = -30 = -114.59(0.5236)sinΦ 0.5 = sinΦ Φ = π/6 and 5π/6. Which...
  29. F

    Simple harmonic motion oscillate. What is the total energy

    Homework Statement The position of a 50 g oscillating mass is given by x(t)=(2.0cm)cos(10t−π/4), where t is in s. If necessary, round your answers to three significant figures. Determine: The total energy. Homework Equations T = 2π/w T = 2π√m/k 1/2kA^2 1/2mv^2 1/2kx^2 The Attempt at a Solution...
  30. T

    Simple Harmonic Motion Question

    Homework Statement I have a question about simple harmonic motion: Where it says " if we denote the ratio k/m with the symbol omega squared ... ": I know it says that they chose omega squared to make the solution simpler, but I mean, to me it doesn't really make sense. Omega is associated...
  31. I

    Choosing unit vectors for harmonic motion problems

    Consider a vertical pendulum affected by gravity (See the pdf file i included). Now i can choose two different opposite directions for my unit vectors which give me different equations. \downarrow : m\ddot x = mg-kx \uparrow : m\ddot x = kx-mg Which of course makes perfect sense, changing...
  32. P

    Simple harmonic motion period with velocity defined

    Homework Statement A mass m is sliding back and forth in a simple harmonic motion (SHM) with an amplitude A on a horizontal frictionless surface. At a point a distance L away from equilibrium, the speed of the plate is vL (vL is larger than zero). Homework Equations What is the period of the...
  33. J

    Simple Harmonic Motion experiment

    Hi pf. I have a question about an experiment. If you lie a ruler horizontally across two supports (one near each end) and then hang a weight in the middle it will undergo SHM if you pull the mass down. If you move the supports in closer it will oscillate with a higher frequency. I just wanted to...
  34. N

    Physics Report Help -- Simple Harmonic motion and Elastic force

    Homework Statement So I have to write a report based on an experiment that I have conducted. I know that my report is connected with Simple Harmonic motion and Elastic force, but I do not know how to describe it in a more efficient/scientific way. Essentially, I am dropping a weight (constant)...
  35. J

    Simple Harmonic Motion of bobble toy

    *note: my previous thread will be deleted because I didn't include relevant equations + I put two unrelated problems in the same thread. 1. Homework Statement A cat bobble head doll consists of a weighted head on top of a spring. When the head hangs straight sown in equilibrium, it is observed...
  36. E

    Simple Harmonic Motion and speed of mass

    Homework Statement [/B] A mass-spring system is oscillating with an amplitude of 10.0 cm. What is the speed of the mass at a location where the kinetic energy of the mass and the potential energy of the spring are equal? I want to know if it's possible to solve for just a number, that is, not...
  37. I

    Simple Harmonic Motion experiment help

    I did an experiment at school, and the experiment SET UP that i did is basically shown in the word attachment link. http://www.schoolphysics.co.uk/age16-19/Mechanics/Statics/experiments/bending_of_a_beam.doc. I have two questions! Question 1:when i did the experiment, I found that with a...
  38. S

    Why is the motion of a piston considered to be simple harmonic motion?

    I know this is simple, but I don't fully understand why the motion of a piston is considered to be simple harmonic? Wouldn't the piston and connecting rod have mass?
  39. A

    Simple Harmonic Motion and angular frequency

    Homework Statement A horizontal plank of mass m and length L is pivoted at one end. The plank's other end is supported by a spring of force constant k (see the figure below). The plank is displaced by a small angle θ from its horizontal equilibrium position and released. Find the angular...
  40. R

    Physics hacksaw problem, harmonic motion

    Homework Statement One end of a light hacksaw blade is clamped in a vise with the long axis of the blade horizontal and with the sides vertical. A 0.665- kg mass is attached to the free end. When a steady sideways force of 20.5 N is applied to the mass it moves aside 13.3 cm from its...
  41. F

    How to find phi in simple harmonic motion

    Given a position vs time graph of simple harmonic motion of an object and using the equation x(t) = xo = A sin (ωt +Φ), how am I supposed to find Φ? I can easily find A and the period (T). I also know T = 2 pi / ω, so I can find ω. But I don't know x(t) and t. I tried finding random points in...
  42. ZARATHUSTRA

    Understanding the Equation of Motion for Simple Harmonic Motion

    For one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, could be obtained by means of Newton's second law and Hooke's law and i don't get this part which...
  43. pyman999

    Simple harmonic motion acceleration

    Homework Statement Homework Equations acceleration = -(2*pi*f)^2 * x, where f is the frequency and x is the displacement from equilibrium. The Attempt at a Solution I thought the acceleration would be greatest when the displacement from equilibrium is greatest, so at point P, but the answer...
  44. pyman999

    Simple harmonic motion question

    Homework Statement http://puu.sh/cAjmp/14ba3df23a.jpg Homework Equations Acceleration at any instant: -(2*pi*f)^2 * x, where x is displacement from equilibrium and f is frequency. The Attempt at a Solution Firstly, I know it can't be D as acceleration would increase as potential energy...
  45. L

    Second-Order Harmonic Motion Equation: Solve as 2 linear diff eqs

    Homework Statement [/B] Write the second-order equation for the harmonic oscillator, y ̈ + ω2y = 0 as two linear ordinary differential equations. What is the analytic solution y(t) if ω = 2π, y(0) = 1 and y′(0) = 0? Homework EquationsThe Attempt at a Solution So, I have to write some...
  46. T

    About velocity equation in simple harmonic motion

    Homework Statement Actually this is not a problem. This is about something i couldn't understand. Homework Equations where wt equals θ The Attempt at a Solution I can understand that x=r.cosθ it is obvious. But i can't understand why Vx=-V.sin(w.t) When i take a triangle from that...
  47. A

    Simple Harmonic Motion equation question: which length and why

    Homework Statement I solved this physics question, but I am unclear about why Amplitude was the amount the spring was stretched by (which should be the new equilibrium point), instead of the amount the person pulled the mass down by (which should be the amplitude). Can anyone help? On your...
  48. B

    Simple Harmonic Motion Pendulum problem

    Homework Statement A simple pendulum of length =30.0cm is released from rest from an angle of θ=10.0∘ to the vertical. Assuming that the pendulum undergoes simple harmonic motion, find its maximum speed. Source: https://isaacphysics.org/questions/accuracy_shm_pendulum_num Homework Equations a)...
  49. NATURE.M

    Comparing Maximum Speeds in Critically Damped and Undamped Harmonic Motion

    Homework Statement A mass on the end of a spring is released from rest at position x0. The experiment is repeated, but now with the system immersed in a fluid that causes the motion to be critically damped. Show that the maximum speed of the mass in the first case is e times the maximum speed...
  50. J

    Interpreting Simple Harmonic Motion Graphs

    Homework Statement Explain the shape of the velocity-displacement and acceleration-displacement graphs for an object undergoing simple harmonic motion. The graph is attached to this thread Homework Equations v = wsqrt(A^2-x^2) where w = angular frequency, A = amplitude and x = displacement...
Back
Top