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.

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  1. D

    Simple Harmonic Motion of a particle

    A particle moves in a straight line so that its position, x cm, from a fixed point O, at time t seconds is given by x=3+12sin(2\pi t)+5cos(2 \pi t). Prove that the particle is undergoing simple harmonic motion, and find x when its speed is 26\pi cm/s. I was fine with the first part of the...
  2. M

    What does 'simple harmonic motion' mean?

    What does 'simple harmonic motion' mean? By definition, it describes any periodic motion that is the result of a restoring force that is proportional to displacement. What does 'periodic' mean here? It means recurring at equal intervals of time? Ususally, the example of SHM is virating...
  3. H

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  4. L

    Simple Harmonic Motion- How Many Times Does the Diaphragm Move Back and Forth?

    Simple Harmonic Motion-Help Please :) Homework Statement A loundspeaker diaphragm is producing a sound for 1.5 s by moving back and forth in a simple harmonic motion. The angular frequency of the motion is 8.50 104 rad/s. How many times does the diaphragm move back and forth? ________...
  5. S

    Simple harmonic motion of a body question

    Homework Statement A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation A=Ai * sin(wt+ (pi/3)) , Where w = pi radians per second, t is in seconds, and Ai = 2.4m. What is the phase of motion at t = 9.4 seconds...
  6. Y

    Harmonic Motion - Bungee Jumping

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  7. R

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  8. I

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  9. N

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  10. B

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  11. C

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  12. F

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  13. K

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  14. S

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  15. R

    Simple Harmonic Motion and equilibrium problem

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  16. H

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  17. D

    Solving for Constants in Simple Harmonic Motion Lab - Tips and Troubleshooting

    Hello all, I have completed a lab for simple harmonic motion, with the goal of finding the constants B, n, and p in the equation T=B*k^n*m^p, where k is the spring constant and m is the mass. I suppose this is more of a math question, because I already have two separate power regressions...
  18. M

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  19. T

    Harmonic motion and the coeffcieient of friction

    1. A tray is moved horizontally back and forth in simple harmonic motion at a frequency of f=2.00Hz. on this tray is an empty cup. obtain the coefficient of static friction between the tray ad cup given that the cup begins slipping when the amplitude of the motion is 0.05m 2. f=kx...
  20. E

    Simple harmonic motion and diatomic molecules

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  21. S

    Solving a Simple Harmonic Motion Problem

    I can't figure out what the heck I need to do for this problem. 3) A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with the time according to the equation A=A sin (wt+ pi/3) Where w=pi radians per second, t is in seconds, and a= 7.6m. What is...
  22. M

    Simple Harmonic Motion Inside earth

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  23. F

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  24. A

    Simple Harmonic Motion and Maximum Speed

    Homework Statement An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk (m = 0.08 g) driven back and forth in SHM at 1.5 MHz by an electromagnetic coil.(a) The maximum restoring force that can be applied to the disk without breaking it is 34,000 N. What...
  25. P

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  26. M

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  27. B

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  28. S

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  29. A

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    Hi i need help with this question. It is focused on simple harmonic equation and the rest of the assignment uses many question which are structure like this. A mass of 16kg on a spring of k = 9.0N/m passes the midpoint of motion with a velocity of 2.0m/s what is the amplitutde? I am unsure...
  30. B

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    I'm supposed to derive x as a function of time for a simple harmonic oscillator (ie, a spring). According to my textbook this is done by using Newton's second law and hooke's law as this: ma=-kx and one gets a differential equation in the second order. I can follow the calculations until...
  31. B

    Simple Harmonic Motion (tuning fork)

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  32. S

    Solving Simple Harmonic Motion Problems| Physics HW

    Homework Statement http://www.physics.umd.edu/courses/Phys122/Noyes/HW/hw1.pdf (pg 3) Homework Equations Im guessing that E = K + U has something to do with it The Attempt at a Solution Not really sure where to start..I tried a few approaches but none of them got me...
  33. V

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    Homework Statement A mass of density d floats in a liquid of density d_L. The mass is then pushed down a distance x and let go. Use Newton's Second Law to demonstrate that the mass will undergo simple harmonic motion. Recall that the SHM equation is d^2x/dt^2 + w^2*x = 0. Assume there is...
  34. T

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    i added a picture which illustrates the situation that i am describing. we put two masses on a spring.each masses weighs m . the luse length of the sping is L. the spring constant is K. both of the bodies (sticked together) are moving in a harmonic motion with an amplitude A. on one...
  35. M

    What is the formula for calculating the maximum speed of a mass on a spring?

    Homework Statement Prove that the maximum speed (Vmax) of a mass on a spring is given by 2(Pi)fA f = period A = Amplitude (compression) Homework Equations Ek = 1/2mv^2 Et = Ek + Ee The Attempt at a Solution So from what I understand, Velocity is maximum when total...
  36. Amith2006

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    Homework Statement # A simple pendulum having charge q, mass m and effective length l is suspended from a rigid support between the plates of a charged capacitor whose plates are kept vertical. What is the time period of oscillation of the pendulum? Homework Equations Time period =...
  37. K

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    Hey, my teacher gave me these two problems for Homework and me nor anybody else in my class has no idea how to do them, any help would be greatly appreciated. 1. a 15.0kg block rests on a horizontal table and is attached to one end of a massless, horizontal spring. By pulling horizontally on...
  38. F

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    Homework Statement While visiting friends at Cal State Chico, you pay a visit to the Crazy Horse Saloon. This fine establishment features a 200- kg mechanical bucking bull that has a mechanism that makes it move vertically in simple harmonic motion. Whether the “bull” has a rider or not, it...
  39. E

    Simple harmonic motion rope swing problem

    Jane wants to swing on a rope across a river. What minimum speed does she need to make it across, and once she's across, what minimum speed does she need to make it back? Here's what's given: mass = 47 kg horizontal wind - call it F - (opposite to her swing) = 120 N horizontal distance (D) =...
  40. M

    Horizontal Harmonic motion and Springs

    Hi all, I am having difficulty with a question. I would like some guidance. QUESTION: A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of 9.5 rad/s. The drawing...
  41. S

    Energy and Simple Harmonic Motion - Part II.

    A horizontal spring is lying on a frictionless surface. One end of the spring is attached to a wall whle the other end is connected to a movable object. The spring and object are compressed by 0.064 m, released from rest, and subsequently oscillate back and forth with an angular frequency of...
  42. S

    Energy and Simple Harmonic Motion.

    A vertical spring with a spring constant of 470 N/m is mounted on the floor. From directly above the spring, which is unstrained, a 0.30 kg block is dropped from rest. It collides with and sticks to the spring, which is compressed by 2.5 cm in bringing the block to a momentary halt. Assuming air...
  43. B

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    A u-tube manometer is half filled with water. The liquid levels are displaced so that one side is higher than the other. The water is then left free to oscillate from side to side. The tube has a cross sectional area of 1.cm^2 and the inital displacement is 0.1m from the rest position, which is...
  44. M

    Simple Harmonic Motion and frequency of vibration

    When a 63 kg person climbs into a 1040 kg car, the car's springs compress vertically by 3.3 cm. What will be the frequency of vibration when the car hits a bump? Ignore damping. Here is the FBD I have drawn: http://img276.imageshack.us/img276/6189/fbdcc2.png Im not even sure if this is...
  45. S

    Understanding the Use of Sin and Cos Formulas in Simple Harmonic Motion

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  46. S

    Finding Angular Frequency for Simple Harmonic Motion - Mass and Rod System

    OK, the answer for this problem seems a bit high to me, so I'm going to ask if it all seems alright. You have a 1m rod of no mass, fixed so that it may rotate about it's center. At the top of the rod is a mass m1 (0.5kg), and the bottom is a mass m2 (1.0kg). Find the angular frequency assuming...
  47. R

    Proving v^2 = n^2 (A^2-x^2) from v dv/dx = -n^2x

    hey guys, just hpoping sum1 could point me in the rite direction...i can't wrk out how to proove v^2=n^2 (A^2-x^2) from v dv/dx = -n^2x obviously you hav to integrate...but i don't know how they get the A into the equation?? what i hav tried is intergating both sides with recpect to x...
  48. L

    Calculate Initial Bullet Speed in SHM with Block-Spring System

    My teacher set us a bunch of pendulum/SHM questions, and I managed to crack them all except for this one which has been bothering me: "A 5.4 g bullet is fired horizontally into a 0.50 kg block of wood resting on a frictionless table. The block, which is attached to a horizontal spring...
  49. F

    Solving Harmonic Motion: Need Help Finding System's Energy

    Hello there! I started a new chapter in my script and have done some problems about harmonic motion. After searching in this forum for a similar problem for ages but without any succees, I need to ask you guys to help me out. Here it is: A toy car of mass 1kg is attached with a spring to a...
  50. B

    Understanding Simple Harmonic Motion: Contradicting Acceleration and Velocity

    When observing the acceleration graph of simple harmonic motion we can see that the acceleration is just the opposite of the elongation. Yet we know that the pendulum velocity is increasing when approaching the equilibrium state. Which means that the motion is accelerated altough the sign of the...
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