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. A

    Finding acceleration, velocity, and time for simple harmonic motion

    Homework Statement A cheerleader waves her pom-pom in simple harmonic motion with an amplitude of .180m and a frequency of .850Hz. a) Find the maximum magnitude of the acceleration and of the velocity. b) Find the acceleration and speed when the pom-pom's coordinate is x=+.090m. c)...
  2. C

    How to solve 2nd order diff. equation for simple harmonic motion

    In my physics class we're talking about LC and LRC circuits, and the equations are analogous to those for SHM. However, I don't see how x=Acos(ωt+\varphi) satisfies m(d^2x/dt^2)+(k/m)x=0. I've never done differential equations and in the book it seemed like the author just guessed and checked...
  3. H

    Approximating a Simple Harmonic motion

    Homework Statement Homework Equations F=ma The Attempt at a Solution I did the first three parts . The last part of this question is quite hard, i tried using Newton's 2nd law of motion but ... here is what happens : T is the tension, as stated in the question . so the equation of...
  4. X

    Simple Harmonic motion and Doppler effect question

    Homework Statement So you're being pushed on a swing by someone who is whistling at a constant 60Hz. At the bottom, Vmax is 4 m/s. Explain what you hear as you swing toward and away from the source of whistling (speed of sound is 343 m/s for this problem). Homework Equations Observed...
  5. J

    Which equation to use in a Simple Harmonic Motion

    Im kind of confused on which acceleration equation to use. A = -(kx)/m or A = -(w^2)Acos[(angular freq)(time) + phase constant] as both of these contribute to SHM. Im guessing I can use the first acceleration equation when i know how far the object stretched and if i don't i...
  6. A

    Simple harmonic motion energy conservation problem

    Homework Statement A mass m hanging on a spring oscillates vertically. If the equilibrium point of the oscillation is a distance d below the relaxed length of the spring and if the amplitude of the oscillation is A, what is the maximum kinetic energy of the oscillation?[b]2. Homework Equations...
  7. Hardik Batra

    Simple Harmonic Motion: Limitations of T

    what is the limitation of T = 2π \sqrt{\frac{m}{k}}
  8. W

    Particle in Simple Harmonic Motion

    Homework Statement Not exactly sure why a time value of 0.500s is given, but I am positive it is why my answer isn't correct: Q. a 1kg object is attached to a horizontal spring. The spring is initially stretched by 0.100m and the object is released from rest there. It proceeds to move...
  9. C

    How Do You Calculate the Time Period of SHM for a Liquid in a U-Shaped Tube?

    Homework Statement We have U-shaped tube filled with liquid , if liquid is displaced through length 'x' find time period of SHM please help me :confused:
  10. B

    Simple Harmonic Motion: Mass on a Spring Homework Solution

    Homework Statement A massless spring hangs down from a support, with its lower end at y=0, where the y-axis is vertical and points downward (normal orientation of y). When a small unknown mass is attached to the spring, the lower end of the spring moves down to a position y_0 for the mass...
  11. H

    Initial displacement in Simple Harmonic Motion

    Homework Statement A meterstick is clamped to a tabletop. The end of the meter stick is deflected downwards a small distance x and is released such the end of the meterstick moves up and down in simple harmonic motion. The meterstick is measured to oscillate up and down 10 times in 5.0...
  12. W

    Question on Simple Harmonic Motion.

    Homework Statement A 100g particle hangs freely at rest on the end of a spring of stiffness 10N/m. If the particle is projected upwards with a speed of 2m/s, find the time taken until it first comes to rest and the distance travelled. Homework Equations Well, there's F = -k.x and of course the...
  13. I

    How can Simple Harmonic Motion have angular frequency?

    It isn't making any intuitive sense. If it isn't moving in circular motion, how can it have angular frequency or speed? Also, v=\pm ω\sqrt { A^{ 2 }-x^{ 2 } } only applies to SHM with springs only, right? Also, does anyone know how to derive this equation below? x=\frac { \pm \sqrt { { { v...
  14. PhizKid

    Simple harmonic motion on an incline

    Homework Statement Homework Equations F = -dU/dx The Attempt at a Solution U = \frac{1}{2}kx^2 + mgxsin\theta \\\\ F = -(kx + mgsin\theta) \\\\ F = -kx - mgsin\theta \\\\ We want to set the force = 0 because that's when the block is in equilibrium with no forces acting on...
  15. T

    Simple Harmonic Motion: Period depends on k coefficient of spring and mass right?

    Period does not depend on amplitude. Correct? I deduced this from the equations for simple harmonic motion: ω=2πf ω=√(k/m)
  16. T

    Difference between simple harmonic motion and stationary sinusoidal wave?

    Their equations are identical. Is there any difference between the two?
  17. T

    Understanding Simple Harmonic Motion: Position and Velocity Functions Explained

    x(t)=Acos(ωt+ϕ)\\v(t)=-ωAsin(ωt+ϕ) I think my physics professor said in one of the lectures that: after setting up your position function by finding amplitude, angular speed, and solving for ϕ by setting t=0 and using the x(0) value given in the question, you need to to set t=0 in the velocity...
  18. Q

    Simple Harmonic Motion: Calculating Mass and Frequency

    Homework Statement A mass is attached to a spring with a force constant of 32N/m. The spring and the mass are set into simple harmonic motion on a frictionless, horizontal surface. The period of vibration of this mass is 0.4 seconds. a) Calculate the object's mass b) Calculate...
  19. H

    Problems of statics, angular motion and simple harmonic motion

    All Questions are shown on pictures. My Calculated answers: A1(a) R= 19.21∠68.7o N (b) E = 19.21∠-111.34o N or = -19.21∠68.7o N <--- Is't either one answer is correct or not? If not, which answer is correct and why? Thanks. A2(b) I = 0.5mr2 = 1.125kgm2 A2(a) k=(I/m)1/2 = 0.212m...
  20. T

    Simple Harmonic Motion Problem 4

    Hi friends the problem is - https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/s480x480/155412_2656530589803_1383873256_n.jpg Attempt - As per the problem states, When the compound system will oscillate in its natural frequency, The frequency of the oscillation will be, √[k/(m...
  21. T

    Simple Harmonic Motion Typical Problem

    Hi friends the problem is - https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/s480x480/60061_2656517749482_1458399262_n.jpg Attempt - As per the problem states, The net force on the particle will be ...
  22. T

    Simple Harmonic Motion problem 1

    Hi friends the problem is - https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-snc6/s480x480/6405_2656465868185_1414230035_n.jpg Attempt - As per the problem states, For the first second equation of SHM, (using x = A sin ωt) a = A sin ω From here I get, sin ω = a/ A...
  23. sankalpmittal

    Question regarding Simple Harmonic Motion

    Homework Statement The two linear simple harmonic motions of equal amplitudes , and angular frequencies ω and 2ω are imposed on a particle along the axes of X and Y respectively. If the initial phase difference between them is π/2 , then find the resultant path followed by the particle...
  24. D

    Simple harmonic motion problem

    Homework Statement This is a 3 part problem and I've successfully solved the first 2 parts, but I don't know what I did wrong in the third part. 1) mass of 346 g on a spring with constant 26.8 N/m on a horizontal + frictionless surface. Amplitude is 6.7 cm. In part 1 i found the total...
  25. W

    Simple Harmonic Motion: Period Dependence on Variables and Curve Fitting

    Homework Statement I'm doing a lab, and they want me to show the dependence of the period on different variables (displacement, mass, and length of pendulum). They ask me to "Fit curves to your plots to show the dependence. Use the curve fits from your plots to devise an equation for...
  26. K

    Simple harmonic motion of a machine part

    Homework Statement A machine part is undergoing SHM with a frequency of of 5hz and amplitude of 1.80cm. How long does it take the part to go from x = 0 to -1.80cm? Homework Equations x = Acoswt The Attempt at a Solution X is given and convert it to metres 0.018. I need to...
  27. D

    Simple Harmonic Motion and equilibrium

    Homework Statement A 93-kg box hangs from the ceiling of a room—suspended from a spring with a force constant of 540 N/m. The unstressed length of the spring is 0.505 m. (a) Find the equilibrium position of the box. (b) An identical spring is stretched and attached to the ceiling and the box...
  28. X

    I do not why the particle does the simple harmonic motion.

    Homework Equations I do not why the particle does the simple harmonic motion. And how to find such innitial condition to satify r decreases continually in time. [b]3. The Attempt at a Solution [/b Is it need to take derivative of r?
  29. H

    Simple harmonic motion of guitar string

    Homework Statement I have a question pertaining to the simple harmonic motion of the midpoint of a guitar string with a frequency of 4.40 x 10^2 Hz and an amplitude of 1.60 mm. I've been asked to deduce the initial displacement, velocity and acceleration of the midpoint of the string, but am a...
  30. D

    Simple Harmonic Motion without damping

    So, simple harmonic motion without damping is described generally by x(t) = Acos(\omega*t +\delta) Which is derived from the differential equation x''+\frac{k}{m}x = 0 We know that A = \sqrt{c_1^2+c_2^2} and tan\delta = \frac{c_1}{c_2} With the differential equation, dealing...
  31. E

    Simple harmonic motion problem help.

    Homework Statement particle experiencing SHM with frequency f= 10 hz find the displacement x at any time t for the following initial conditions. @ t=0 x=0.25m v=0.1 m/sHomework Equations x=Asin(ωt+∅) v=Aωcos(ωt+∅)The Attempt at a Solution So with frequency I find ω which then is subbed into...
  32. S

    Understanding Simple Harmonic Motion: The Role of Frequency in Wave Equations

    I was reading a book on wave and found that when they derive the equation of shm from the equation force varies with negetive displacement , they had taken a propotionality constant to make the force and displacement equal and they had taken frequency of the shm as the constant . So my question...
  33. T

    Simple Harmonic Motion: Two Springs One Mass

    Homework Statement Two springs each have spring constant k and equilibrium length (L). They are both stretched a distance (L) and attached to a mass m and two walls. At a given instant, the right spring constant is somehow magically changed to 3k (the relaxed length remains L). what is the...
  34. M

    Lorentz Force or Simple Harmonic Motion

    So my friend and I were going through problems and this came up... Consider 3 straight, infinitely long, equally spaced wires (with zero radius, separated each by a distance d), each carrying a current I in the same direction. blah blah blah... part c) asks us... If the middle...
  35. C

    Simple harmonic motion vs. harmonic motion

    I know that simple harmonic motion is a type of periodic motion where the restorative force is directly proportional to the displacement so that the time evolution is sinusoidal but is there such a thing as just harmonic motion? 0r is harmonic motion just short for simple harmonic motion?
  36. K

    Finding Force and Distance in Simple Harmonic Motion Problem

    Homework Statement A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest: a.) find the force between the bottom of the box and the block as a function of time...
  37. B

    Simple harmonic motion - Find amplitude given period

    Homework Statement A block rides on a piston that is moving vertically with simple harmonic motion. (a) If the SHM has period 2.65 s, at what amplitude of motion will the block and piston separate? Homework Equations x(t)=xmcos(ωt + ∅) a(t)=-w2xmcos(ωt + ∅) Where xm is the amplitude...
  38. C

    Simple harmonic motion + rate of changes

    A bucket of mass 2.0 kg containing 10 kg of water is hanged on a vertical ideal spring with constant 125 N/m, oscillating up and down with an amplitude equal to 3.0 cm. Suddenly arises a leaky in the bottom of the bucket so that the water flows at constant rate of 2.0 grams/s. When the bucket...
  39. S

    Simple Harmonic Motion, Force as a Function of Time

    Homework Statement A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest: a.) find the force between the bottom of the box and the block as a function of time...
  40. S

    Simple Harmonic Motion (SHM) question check

    Homework Statement A metal sphere of mass 0.20kg is hung from a helical spring whose top end is clamped. the sphere is displaced by 0.030m below its equilibrium position, and then released. 20 cycles of oscillation, of amplitude 0.030m, occur in a time of 12.0s. calculate; (I) the spring...
  41. L

    Simple harmonic motion and damping

    I have to solve the following D.E. which describes how the amplitude of oscillation r, changes with time. r=f(t) \frac{dr^{2}cos^{2}t}{dt}=rsint How do I find r?
  42. M

    Simple Harmonic Motion: Displacement after s seconds

    The question is: A 56.0 kg bungy-jumper hangs suspended from her bungy-cord, at rest. She is displaced from this position by 15.0 m downward, and then released. She bounces up and down, with a period of 5.800 s. Assume the woman undergoes simple harmonic motion, described by y(t) = X cos(2...
  43. S

    Particle moving in Simple Harmonic Motion

    Homework Statement A particle moving in simple harmonic motion with a period T = 1.5 s passes through the equilibrium point at time t0 = 0 with a velocity of 1.00 m/s to the right. A time t later, the particle is observed to move to the left with a velocity of 0.50 m/s. (Note the change in...
  44. H

    Simple harmonic motion spring force constant help

    Homework Statement A spring is hung vertically from a support. A mass of 4.5 kg is hung from the lower end of the spring and is slowly lowered a distance of 22.0 cm until equilibrium is reached. This mass is then lowered to a point 15.0 cm below the equilibrium point and is then released...
  45. S

    Simple Harmonic Motion using total mechanical energy

    Homework Statement A 250 gram mass is connected to a spring and executes simple harmonic motion. The period of motion is 0.5 seconds and the total mechanical energy is 0.50J. What is the amplitude of motion? Homework Equations ΔU = 1/2kx2 The Attempt at a Solution I get 1/2kx2 =...
  46. J

    Simple Harmonic Motion Test Question

    I've been set this question by my tutor and I'm having difficulty doing it. A mass of 2 kg is hung from the lower end of a vertical spring and extends it by 40 cm. The mass is now pulled down a further 20 cm and is then released from rest so that it oscillates about the equilibrium position...
  47. O

    Simple Harmonic Motion for a block-spring system

    Homework Statement If the phase angle for a block-spring system in SHM is π/5 rad and the block's position is given x = xm cos(ωt + phi), what is the ratio of the kinetic energy to the potential energy at time t = 0? Homework Equations PE = (1/2)*k*[(max amplitude)^2]*cos^2(ωt + phi)...
  48. Jalo

    Simple harmonic motion - Springs

    Homework Statement I have trouble determining the system of forces in systems with strings like the following: Homework Equations The Attempt at a Solution My guess is it is: x1=L/3 x2=2L/3 mass 1: -kx1+k(x2-x1)=m1a1 mass 2: -k(x2-x1)+kx1=m2a2 I'm not sure...
  49. S

    Simple harmonic motion problem

    Homework Statement A mass is oscillating on a spring with simple harmonic motion. Its amplitude is 0.80m and its maximum speed is 1.5m/s, at the point of equilibrium. What is the speed of the mass at 0.60m? Is there enough information to answer this question? The answer given is 0.75m/s...
  50. M

    A body moving with simple harmonic motion has an amplitude of 1

    A body moving with simple harmonic motion has an amplitude of 1 meter and the time for one complete oscillation is 2 seconds . Determine the velocity and acceleration of the body after 0.4 second from the mean position ? this is the answer : Vx = w root(r^2-x^2) ax=w^2.X w= 2Pi/t =...
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