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. ~christina~

    Motion of object (simple harmonic motion?)

    Homework Statement A ball dropped from height 4.00m makes an ellastic collision with the ground. Assuming no mechanical energy is lost to air resistance. a) show that the motion is periodic b) determine period of motion c) is the motion simple harmonic? Homework Equations...
  2. qspeechc

    How Can We Determine the Motion of a Compound Harmonic Mechanical System?

    Homework Statement http://img209.imageshack.us/my.php?image=springzu4.png Determine the motion of this mechanical system satisfying the initial conditions :- y1(0) = 1 y2(0) = 2 y1'(0) = -2*sqrt(6) y2'(0) = sqrt(6) Hint : there are 4 different methods you can use to solve this...
  3. L

    Simple Harmonic Motion in daily life

    Do you think that the daily movement of a student from home to university then again from university to home is an example of simple harmonic motion ? Please give the arguments in support of your point of view.
  4. J

    Question abou Simple Harmonic Motion

    Homework Statement A spring mass system has the following parameters: Mass m=1 kg, spring constant k=100 N/m. The oscillations are started by initially displacing the mass so that the spring is compressed by 0.5 cm and releasing it from rest. What is the speed of the mass (in m/s) when it...
  5. T

    Total energy of a spring-mass system (harmonic motion)

    Hi all. I've this problem and I'm stuck on the part where I have to find the total energy. Homework Statement A 507 g mass oscillates with an amplitude of 10 cm on a spring whose spring constant is 20 N/m. At t =0s the mass is 5.0 cm to the right of the equilibrium position and moving to the...
  6. L

    SHM - Finding Distance and Direction of Oscillating Particles

    SHM - Simple Harmonic Motion Question Homework Statement Two particles oscillate in SHM along a common straight-line segment of length A. Each particle has a period of 1.5s, but they differ in phase by π/6 rad. a. How far apart are they 9in terms of A) 0.50s after the lagging particle...
  7. S

    Average Kinetic & Potential Energy in Simple Harmonic Motion

    in SHM average K.E when done w.r.t to time is equal to average potential energy calculated w.r.t to time. but today in class when my sir asked me to to prove average K.e = average P.E I just tried integrating it w.r.t to displacement and then divided it with A , I thought this gives us av...
  8. D

    Simple Harmonic Motion - Floating Object

    [SOLVED] Simple Harmonic Motion - Floating Object Homework Statement The problem states that an object is pushed down and released. It is floating. The density is P(block) and the area is A and its height is h The fluid's density is P(fluid) The Problem asks to show that it executes...
  9. P

    Harmonic Motion 2: Sally & Mommy Ride the Least Exciting Carnival Ride

    The world's least exciting carnival ride consists of a cloth sling (of negligible mass) hanging by a spring of force constant k = 225 N/m. Children sit in the sling and bob up and down slowly. How exciting ... Little Sally tries the ride. She gets into the sling, and, after Cletus the Carny...
  10. P

    Finding the Period of Oscillation for an Elevator After a Minor Earthquake

    An elevator of mass M = 300 kg hangs at the end of a long, thin steel cable: it has length L = 96 m and diameter d = 3 mm. A minor earthquake shakes the entire building. After the quake passes, the elevator continues to bob up and down for a long time. What is the period of oscillation? i used...
  11. S

    Why Does Adding 2π to the Phase Angle Yield Equivalent Solutions in SHM?

    In simple harmonic motion example there is a question velocity max is given velocity at time = 0 is given (which is not equal to maximum velocity --> not at equilibrium point at time=0) graph is also given of the velocity function IT asks to find the phase angle in the solution they...
  12. V

    Simple Harmonic Motion of a body

    Homework Statement A body is in simple harmonic motion of amplitude 0.50m and period 4pie seconds. What is the speed of the body when the displacement of the body is 0.30 m? Homework Equations Would it be x=Acos2(pie)ft ? The Attempt at a Solution I tried substituing in x=...
  13. M

    Derivation of Simple Harmonic Motion for a Spherical Bowl

    Problem: Prove that it is valid to model a particle in a smooth hemispherical bowl as a simple pendulum, provided its maximum displacement is small. Answer: Usually, a FBD is used along with Newton's 2nd, and then the small angle approximation is used twice (once for siintheta in the weight...
  14. M

    How Do You Calculate Angular Frequency in Simple Harmonic Motion?

    Homework Statement A horizontal plank (m = 2.0 kg, L = 1.0 m) is pivoted at one end. A spring. (k = 1000N/m) is attached at the other end find the angular frequence for small oscillations? Homework Equations w=(k/m)^0.e\5 The Attempt at a Solution w= (1000/2)^0.5 i have no idea...
  15. M

    Simple harmonic motion of a spring

    Homework Statement A horizontal plank (m = 2.0 kg, L = 1.0 m) is pivoted at one end. A spring (k = 1.0 x 10 3 N/m) is attached at the other end, as shown in the figure. Find the angular frequency (in rad/s) for small oscillations Homework Equations w = (mgd/I)^0.5 I= 1/3 ML^2...
  16. M

    Energy Problem involving simple harmonic motion

    Homework Statement The motion of a particle is described by x = 10 sin (piet +pie/2 ). At what time ( in second ) is the potential energy equal to the kinetic energy ? Homework Equations KE = 1/2 mv^2 PE=1/2 Kx^2 The Attempt at a Solution V=pie10cos(piet + pie/3) V^2 = pie^2...
  17. L

    Understanding Simple Harmonic Motion: Equations and Parameters Explained

    I'm confused on part of an AP Physics lab on "Simple Harmonic Motion from a Force Perspective." Using a hanging spring & mass, motion detector, and CBL unit/Ti-83 graphing calculator, we used the calculator's graphs to create equations that included the amplitude, angular frequency, the phase...
  18. C

    Energy in Simple Harmonic Motion

    A 1.3 kg object oscillates with simple harmonic motion on a spring of force constant 410.0 N/m. The maximum speed is 0.7 m/s. What is the total energy of the object and the spring? Do I just set it up like this: 1/2*410*x^2=1/2*1.3*.7^2 to get the max x Then do I just add them up
  19. V

    Simple Harmonic Motion of an earthquake

    [SOLVED] Simple Harmonic Motion Homework Statement Four people, each with mass of 71.1 kg, are in a car with a mass of 1180 kg. An earthquake strikes. The vertical oscillations of the ground surface make the car bounce up and down on its suspension springs, but the driver manages to pull of...
  20. J

    Simple Harmonic Motion of an ideal spring

    Homework Statement An ideal spring has a spring constant k = 29 N/m. The spring is suspended vertically. A 1.4 kg body is attached to the unstretched spring and released. It then performs oscillations. (a) What is the magnitude of the acceleration of the body when the extension of the...
  21. T

    Simple Harmonic Motion and parallel-axis-theorem

    Hello, I have problems solving the following two problems: 1)You measure the period of a physical pendulum about one pivot point to be T. Then you find another pivot point on the opposite side of the center of mass that gives the same period. The two points are separated by a distance L. Use...
  22. A

    Springs and simple harmonic motion

    Homework Statement If the initial period is 3.0 s and the mass is reduced to 1/3 of its initial value, what is the new period?Homework Equations Possibly T=2pi*squareroot(m/k)The Attempt at a Solution The solution is something close to 1.73. I have no idea what equation to use, even. Any...
  23. D

    Simple Harmonic Motion Reference Circle

    Homework Statement Through simple harmonic motion produced on a trampoline Ivan ossilates freely, with a period of 0.85s. On a reference circle show Ivans position after 1/8th of a cycle. Label (and solve) the distance of this position from the equilibrium position.(Max displacement is...
  24. C

    Simple Harmonic Motion and Wave Motion

    Hi, I was wondering if anyone could explain Simple Harmonic Motion. My physics teacher has tried and I have read the parts in the book, but I am still confused. I know how to find the amplitude from the standard form equations, but I really just don't understand how to get the period and...
  25. A

    Simple Harmonic Motion - Period (T)

    [SOLVED] Simple Harmonic Motion - Period (T) 1. A pendulum oscillates with a period T. If both the mass of the bob and the length of the pendulum are doubled, the new period will be _____. 2. T = 2(pi) x rad (k/m) 3. Since L is not a part of the equation, it shouldn't affect...
  26. D

    Simple Harmonic Motion with 2 Springs attached to a Dynamics Cart

    I'm trying to write a lab report but I cannot figure out how to derive the formulas for my Theories and Derivations section. Basically, the set-up was this: Two springs were attached to either ends of a dynamics cart. Each spring was then attached to a bumper at either end of the dynamics...
  27. R

    What is the relationship between A_{c} and A_{s} in simple harmonic motion?

    1. Homework Statement (a) Show that A_{0}cos(\omegat+\delta) can be written as A_{s}sin(\omegat)+A_{c}cos(\omegat), and determine A_{s} and A_{c} in terms of A_{0} and \delta. (b) Relate A_{c} and A_{s} to the initial position and velocity of a particle undergoing simple harmonic motion...
  28. A

    Calculating Speed in Simple Harmonic Motion

    [SOLVED] Simple Harmonic Motion This is the question I was given on my assignment, I can't seem to get it, bad prof so I am trying to teach all of this to myself, but this stuff is a bit confusing. From what I have tried and gather from examples in mt text, sub in .120s and solve but that is...
  29. B

    Simple Harmonic Motion of a cart

    Homework Statement A 0.620-kg cart is moving down an air track with a speed of 2.33 m/s when it collides with a spring. The spring is initially at its equilibrium position, but the cart compresses the spring. It takes 0.0780s after the cart hits the spring for the cart to come to a stop. The...
  30. B

    Harmonic Motion Homework: Find x(t) from Rest at x=11 cm

    Homework Statement A 171 g object on a spring oscillates left to right on a frictionless surface with a frequency of 3.00 Hz and an amplitude of 11.0 cm. (a) What is the spring constant? N/m (b) If the object starts from rest at x = 11.0 cm at t = 0 and the equilibrium point...
  31. C

    Help with a Simple Harmonic Motion problem

    1. A 25.0g bullet strikes a .600kg block attached to a fixed horizontal spring whose spring constant is 6.70x10^3 and sets it into vibration with an amplitude of 21.5cm. What is the speed of the bullet before impact if the two objects move together after impact?2. V=A\sqrt{k/m} 3. I used the...
  32. C

    Springs, Simple Harmonic Motion

    1. A 25.0g bullet strikes a .600kg block attached to a fixed horizontal spring whose spring constant is 6.70x10^3 and sets it into vibration with an amplitude of 21.5cm. What is the speed of the bullet before impact if the two objects move together after impact?2. V=A\sqrt{k/m} 3. I used the...
  33. N

    Simple Harmonic Motion Lab Data Analysis

    Here is the problem I am having: Professor told me to find the spring constant using our slope of the graph. Now the graph that I did on the excel went something like this: On the X-axis of the graph was the weight of the hanging mass in Newtons and on the Y-axis of the graph was the...
  34. G

    How to Find the Energy in Harmonic Motion?

    Homework Statement Problem 60 in attached image: Homework Equations E = U + K E = \frac{1}{2}kx^{2} + \frac{1}{2}mv^{2} + \frac{1}{2}Iw^{2} w = \sqrt{\frac{k}{m}} x(t) = Acos(wt) Equation 13.3 they are referring to in the book: m(\frac{d^{2}x}{dt^{2}}) = -kx ---->...
  35. J

    Simple harmonic motion equation

    Homework Statement An object is undergoing simple harmonic motion. The graph shows the position of the object as a function of time. What is the first time after t = 0 s when the speed reaches a maximum? http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype26/shm.47.jpeg...
  36. C

    Finding Amplitude-simple harmonic motion

    Homework Statement Simple harmonic motion problem. The number of daylight hours in a day is harmonic. Suppose that in a particular location, the shortest day of the year has 6.5 hours of daylight and the longest day of the year has 17.5 hours. Then, we can model its motion with the function...
  37. M

    Effects of Air Resistance on Simple Harmonic Motion Graphs

    Homework Statement I'm given the position vs. time, velocity vs. time, acceleration vs. time, and energy vs. time graphs for a simple harmonic motion, and I want to know what would happen to those graphs if air resistance is included? Homework Equations N/A The Attempt at a Solution...
  38. G

    Simple Harmonic Motion question

    Homework Statement A spring is standing upright on a table with its bottom end fastened to the table. A block is dropped from a height 3 cm above the top of the spring. The block sticks to the top end of the spring and then oscillates with an amplitude of 10 cm. What is the oscillation...
  39. I

    Simple Harmonic Motion and Battleships

    Hi, Recently, a friend and I were watching a 2nd world war film where a battleship was shelling land based fortifications. The discussion arose on how the ship (which was moving up and down due to the waves in the sea) could accurately target the fortifications. I remember being told that...
  40. T

    Simple harmonic motion and frequency

    Homework Statement Consider a simple harmonic oscillator made of a mass sliding on a frictionless surface, and attached to a massless linear spring. Which of the following statements are true/false? True False Quadrupling the mass will halve the frequency. True False Doubling the spring...
  41. D

    Simple Harmonic Motion: Mass on a spring

    Homework Statement A massless spring with spring constant 27.7 N/m hangs vertically. A body of mass 0.31 kg is attached to its free end and then released. Assume that the spring was unstretched before the body was released. How far below the initial position does the body descend...
  42. H

    Simple Harmonic Motion of a particle of mass

    Homework Statement A particle of mass m is constrained to move along the x-axis. The potential energy is given by, V (x) = a + bx + cx2, where a, b, c are positive constants. If the particle is disturbed slightly from its equilibrium position, then it follows that (a) it performs simple...
  43. A

    Simple harmonic motion of ornament on tree

    Homework Statement A holiday ornament in the shape of a hollow sphere with mass 2.0×10−2 kg and radius 5.5×10−2 m is hung from a tree limb by a small loop of wire attached to the surface of the sphere. If the ornament is displaced a small distance and released, it swings back and forth as a...
  44. A

    Approximation to simple harmonic motion.

    [SOLVED] Approximation to simple harmonic motion. Homework Statement A small mass m, which carries a charge q, is constrained to move vertically inside a narrow, frictionless cylinder. At the bottom of the cylinder is a point mass of charge Q having the same sign as q. Show that if the mass m...
  45. P

    Finding harmonic motion equation

    Homework Statement A particle moves along the x axis. It is initially at the position 0.27 m, moving with velocity 0.14 m/s and acceleration -0.320 m/s2. First, assume that it moves with constant acceleration for 4.50 s. (a) Find its position. (b) Find its velocity at the end of this time...
  46. A

    Simple Harmonic Motion of springs

    [SOLVED] Simple Harmonic Motion Homework Statement A mass rests on a frictionless horizontal table and is connected to rigid supports via 2 identical springs (which obey Hooke's law). Each spring is stretched to a length (l) considerably greater than its rest length. At rest, the mass is...
  47. K

    Simple harmonic motion: platform

    Homework Statement A point mass rests on a horizontal platform which can be made to describe vertical s.h.m. of amplitude 0.10m and frequency 2.0 Hz. The mass makes contact with the platform as it rises from its lowest point. At what point, if any, will this contact be lost? Homework...
  48. P

    E&M Electric Fields (Harmonic Motion?)

    E&M Electric Fields (Harmonic Motion?) This problem comes out of "Physics (for scientists and engineers w/ modern physics) Volume 2 7th Edition" by Serway/Jewett Review Problem Two identical particles, each having charge +q, are fixed in space and separated by a distance d. A third particle...
  49. O

    How Does Archimedes's Law Apply to Harmonic Motion?

    Hi everyone, I have 2 small questions for you, both related to (simple) harmonic motion. First, I have this diagram: http://img227.imageshack.us/img227/8530/archimedesvu2.jpg The mass of the cylinder is m, the area of a cut is S, and the water's density is p (supposed to be the Greek rho but p...
  50. S

    The addition of three simple harmonic motion

    [SOLVED] the addition of three simple harmonic motion Homework Statement A particle is simultaneously subjected to three simple harmonic motions, all of the same frequency and in the x direction. If the amplitudes are 0.25, 0.20 and 0.15 mm, respectively, and the phase difference between...
Back
Top