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. 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##...
  2. 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...
  3. asteeves_

    Calculating Amplitude in Simple Harmonic Motion

    I have encountered two separate review problems that have to do with finding a value for amplitude and I am really struggling with it. 1. Homework Statement Question 1- A mass of 3kg is free to move on a horizontal frictionless surface and attached to a spring of k=15 N/m. It is displaced...
  4. A

    Why are there modes in cantilever beam oscillation equations

    I'm doing an experiment measuring the relationship between length of a cantilever beam and period of oscillation when I twang it on one end, but I can't seem to understand the equation. The equation for measuring frequency is given here:https://www.hindawi.com/journals/amse/2013/329530/ but I...
  5. 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...
  6. 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...
  7. anon11

    Ball on a Turntable Simple Harmonic Motion

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  8. L

    Position vs time graph simple harmonic motion phase constant

    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...
  9. A

    Energy changes in mass spring system

    Why is the kinetic energy vs time curve of a mass spring system is just a modulus of respective velocity time curve. How can we prove it mathematically ?
  10. 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...
  11. 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.
  12. Vanessa Avila

    Finding time of how long the block travels (SHM)

    Homework Statement A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. When the amplitude of the motion is 0.090 m , it takes the block 2.52 sto travel from x= 0.090 m to x= -0.090 m . If the amplitude is doubled, to 0.180 m , how long does...
  13. Vanessa Avila

    The ball's maximum speed relative to the vehicle?

    Homework Statement Inside a NASA test vehicle, a 3.50-kg ball is pulled along by a horizontal ideal spring fixed to a friction-free table. The force constant of the spring is 226 N/m . The vehicle has a steady acceleration of 5.00 m/s2, and the ball is not oscillating. Suddenly, when the...
  14. 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 =...
  15. Vanessa Avila

    Simple Harmonic Motion: Finding displacement at given time t

    Homework Statement A 1.10 kg mass on a spring has displacement as a function of time given by the equation x(t)=(7.40cm)cos[(4.16rad/s)t−2.42rad]. Find the position of the mass at t=1.00s; Homework Equations x = Acos(ωt+∅) The Attempt at a Solution I tried to just plug in the time t in that...
  16. P

    Solving Harmonic Motion: Find Equilibrium Points & Frequency

    Homework Statement A potential energy function for a particle moving in one-dimension is given as: V (x) =k1x^2/(2)+k2/x (a) Locate all the equilibrium points. (b) Show that the motion is always periodic for any amount of total energy. (c) What is the frequency f the motion if the amplitude of...
  17. Mayan Fung

    Introducing SHM to high school students

    I need to introduce Simple Harmonic Motion to a group of high school students studying physics. They don't know anything about differential equation except the method of separation of variables. Also, they have limited knowledge on complex numbers like eiωt. However, I don't want to just give...
  18. Wes Ellgass

    Simple harmonic motion calculations from doubling the mass.

    Homework Statement What will the new amplitude be if A=.117m and the mass is 0.1kg. The spring constant is 3.587N/m and the mass is then doubled. What is the new velocity max? What is the acceleration max? Homework Equations Fnet= -kx, vmax=A(ω), ω= √k/m The Attempt at a Solution...
  19. Elvis 123456789

    Mass within a box hung from a spring

    Homework Statement A block of mass m is placed inside a box of mass M , which is then hung from a spring with spring constant k. The system is pulled down some distance d and released at time t =0. Determine the reaction force between the block and the bottom of the box as a function of time...
  20. A

    Second Order Runge Kutta for Simple Harmonic Motion

    Homework Statement The ordinary differential equation describing shm is d^2x/dt^2=-w^2x where x is the displacement, t is the time and w is the frequency. If x=0 at t=0, the analytical solution is x=Asin(wt), where A is the amplitude. 1) Rewite equation 1 as two first oder ode's suitable for...
  21. moenste

    Body on a spring: expression for the period T

    Homework Statement (a) A body of mass m is suspended from a vertical, light, helical spring of force constant k, as in Fig. 1. Write down an expression for the period T of vertical oscillations of m. (b) Two such identical springs are now joined as in Fig. 2 and support the same mass m. In...
  22. E

    How Is the Period of a Pendulum Affected by Its Length?

    To increase the period of oscillation of a pendulum in 1 second, it is needed to increase the length of it in 2 meters. Calculate, in seconds, of the initial period of oscillation of the pendulum. I found this question online a few minutes ago. I have not learned this in physics class yet so...
  23. moenste

    Particle moving with simple harmonic motion

    Homework Statement A particle moves with simple harmonic motion in a straight line with amplitude 0.05 m and 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)] which...
  24. Pao44445

    B Simple Harmonic Motion: Finding Amplitude, Velocity, and Acceleration

    I am studying about SHM but I don't know how to find an amplitude,velocity,acceralation of motio. I know the formula but I don't understand where it came from x = Asin(omega(t))
  25. J

    Simple Harmonic Motion - Getting Acceleration from Velocity

    Homework Statement I am doing an experiment where I am measuring the force a speaker is exerting when it is driven by a certain voltage and frequency, so my voltage and frequency values are known. I am assuming the speaker is undergoing SHM and I am measuring its peak to peak velocity...
  26. Vanessa Le

    Simple Harmonic Motion with Rotational Inertia

    Homework Statement One end of a light spring with force constant k = 100 N/m is attached to a vertical wall. A light string is tied to the other end of the horizontal spring. the string changes from horizontal to vertical as it passes over a pulley of mass M in the shape of a solid disk of...
  27. R

    Non-Harmonic Pendulum: Calculating Gravity g

    If the Pendulum doesn't follow Harmonic Motion can we still use the formula 1) T = 2π Root(L/g) ? 2) If not, how can I calculate gravity g?
  28. M

    MHB Simple Harmonic Motion: 5kg Particle Suspended by 500 N/m String

    A particle of mass 5 kg is suspended from a fixed point by a light elastic string which hangs vertically. The elastic constant of the string is 500 N/m. The mass is pulled down a vertical distance of 20 cm from the equilibrium position and is then released from rest. (i) Show that the particle...
  29. TheCapacitor

    Measuring young's modulus from simple harmonic motion

    Homework Statement I was doing this experiment: http://practicalphysics.org/shm-cantilever.html I'm interested in the derivation of the result ω^2 = Exy^3 / 4*M*L^3. I tried to think where it comes from. How do we even start to derive k from the equation mg = KS where S is the delta in the...
  30. M

    MHB When does the elastic string become slack in simple harmonic motion?

    A particle of mass m is suspended from a point p on the ceiling by means of a light elastic string of natural length d and elastic constant of 49m/d. it is pulled down a distance 8d/5 below p and released from rest. (i) show it will preform SHM as long as the string remains taut. (ii) find in...
  31. Erenjaeger

    Simple harmonic motion problem

    Homework Statement A 45.0-g object connected to a spring with a force constant of 40.0 N/m oscillates with an amplitude of 6.00 cm on a frictionless, horizontal surface. a) find the total energy of the system (mJ)[/B]Homework Equations 1/2KA^2 [/B]The Attempt at a Solution Is the force...
  32. Clara Chung

    Simple Harmonic Motion: Pendulum Oscillation Calculation

    Homework Statement A pendulum of length 2.0 m makes small angle oscillations with an amplitude of 15 degrees. a) Find the time required for the bob to oscillate from 5 degrees to 10 degrees to the right. b)Calculate the velocity and acceleration at these two positions. Homework Equations ω^2...
  33. A

    Simple harmonic motion (with calculus)

    Homework Statement An object with mass m undergoes simple harmonic motion, following 2 perpendicular directions, described by the equations: x=a cos (wt), a>0, y=b cos (2wt), b>0 a) find the equation of the trajectory b) find the speed at any given time (so having t as a variable) c) the...
  34. B

    Kinetic Energy from a Simple Harmonic motion and spring

    Homework Statement A 0.26-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 190 N/m. The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes...
  35. Nipuna Weerasekara

    A Simple Harmonic Motion Question

    Homework Statement As in the given picture, the cylinder is drowned (not completely drowned as in partially drowned) in water. The cylinder is attached with a spring which has the spring constant of 200 N/m. The spring has attached to a unmovable point in the ceiling. The weight of the...
  36. MaxBicknell

    Simple harmonic motion solved for time

    Homework Statement A particle of mass 0.50 kg performs simple harmonic motion along the x-axis with amplitude 0.55m and period 4.3 seconds. The initial displacement of the particle is -0.30 m and it is traveling in the positive x-direction. The phase constant of the motion (Φ) = -2.15 rad...
  37. ryanuser

    Simple harmonic motion problem

    Homework Statement A body performaning simple harmonic motion has a displacement x given by the equation x= 30 sin 50t, where t is the time in seconds. what is the frequency of the oscillation? Answers are: A. 0.020Hz B. 0.13Hz C. 8.0Hz D. 30Hz E. 50Hz (correct...
  38. RoboNerd

    Graphs relating to simple harmonic motion

    Homework Statement Homework Equations None. The Attempt at a Solution Hi everyone. Apparently 5 is the right answer, although I chose D. Could anyone please weigh in with their thoughts about why 5 is right and my answer is apparently wrong? Thanks!
  39. J

    Need help for question about spring oscillation

    Homework Statement I want to know why the answer is C not B. Thanks. Homework Equations F=kx The Attempt at a Solution
  40. i_hate_math

    Simple Harmonic Motion and Energy Problem

    Homework Statement In the figure, block 2 of mass 2.40 kg oscillates on the end of a spring in SHM with a period of 26.00 ms. The position of the block is given by x = (1.80 cm) cos(ωt + π/2). Block 1 of mass 4.80 kg slides toward block 2 with a velocity of magnitude 6.90 m/s, directed along...
  41. i_hate_math

    Easy Simple Harmonic Motion Problem

    Homework Statement Two particles oscillate in simple harmonic motion along a common straight-line segment of length 1.5 m. Each particle has a period of 1.5 s, but they differ in phase by π/5 rad. (a) How far apart are they 0.46 s after the lagging particle leaves one end of the path? (b) Are...
  42. Niall103

    SHM Q&A: Find Period given Max Speed & Acceleration

    << Mentor Note -- thread moved from the technical forums, so no HH Template is shown >> Hello, So I've been doing old practice questions on SHM to revise, and just been frustrating myself on this one for a bit. The question is: "An object vibrating with simple harmonic motion has a maximum...
  43. S

    Simple Harmonic Motion Problem

    Homework Statement A 12.0-N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as a function of time t is given by: y(t)=4.50cmcos[(19.5s−1)t−π/8]. (a) What is the spring constant of the spring? (b) What is the maximum...
  44. C

    Periodic Time Calculation for Simple Harmonic Motion with a Spring

    Homework Statement A 0.61 kg mass attached to a spring (k = 27 N m-1) is performing SHM on a smooth horizontal surface. Calculate the periodic time of these oscillations. Homework Equations ω=2π/T ω=2πƒ The Attempt at a Solution I think I need to find out the angular frequency ω of the...
  45. Z

    Finding mass of an object on a spring, given Frequency

    Homework Statement A mass m at the end of a spring oscillates with a frequency of 0.84 Hz . When an additional 730 g mass is added to m, the frequency is 0.65 Hz . Homework Equations f*2pi = w w = (k/m)^1/2 f = (1/2pi)*(k/m)^1/2 The Attempt at a Solution I simply used the third equation...
  46. L

    SHM: Gravity-Powered Train (Brace Yourself)

    Homework Statement [/B] Two cities are connected by a straight underground tunnel, as shown in the diagram. A train starting from rest travels between the two cities powered only by the gravitational force of the Earth, F = - \frac{mgr}{R}. Find the time t_1 taken to travel between the two...
  47. M

    What is the relationship between force and time in simple harmonic motion?

    For the lab I have to find the spring constant and how force relates to time with simple harmonic motion. To find the spring constant, I used hooke's law and compared different added masses to the stretch from the equilibrium position. When I graphed that, the slope was the spring constant since...
  48. E

    Simple harmonic motion of particles

    Homework Statement Two particles are executing simple harmonic motion of the same amplitude A and frequency ω along the x-axis. Their mean position is separated by distance X0 (X0 > A). If the maximum separation between them is (X0 + A), the phase difference between their motion is My answer...
  49. H

    What are the uses of a bifilar pendulum?

    how is a bifilar pendulum useful in everyday life and why do we study about it?
  50. vetgirl1990

    Finding amplitude from simple harmonic equation function

    Homework Statement The periodic motion is given in the form: f(t) = Acos(wt+φ) What is the amplitude and phase constant for the harmonic oscillator when: (a) f(t) represents position function x(t) (b) f(t) represents velocity function v(t) (c) f(t) represents acceleration function a(t)...
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