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. L

    Simple harmonic motion trouble

    hey guys I am having trouble figuring out if something is undergoing simple harmonic motion. i know that for an object to be executing simple harmonic motion, its position and velocity must follow a sin curve...but I am still having trouble. ok for example, a question on a worksheet said "a...
  2. P

    How to Calculate the Spring Constant for Simple Harmonic Motion?

    simple harmonic motion ? hey guys, I am having troube with this problem a vertical spring stretches .25m when a 2kg weight is hung from it. If that weight were oscillating up and down, how long would it take to complete 10 cycles? so first i tried to find k by using...
  3. V

    Simple Harmonic Motion Oscillations

    Hi, So I'm having a little bit of trouble answering a couple of simple questions regarding simple harmonic motion... [Image] All of this is regarding the really simple image ^ Oscillations are not always described by equations; you should also be able to analyze the graphical...
  4. J

    Harmonic Motion Help: Solving After Collision

    I am having trouble with this problem: A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is oscillating on a horizontal frictionless surface with an amplitude of 2.00 m. A 6.00-kg object is dropped vertically on top of the 4.00-kg object as it passes...
  5. C

    Help with Simple Harmonic Motion

    I need help on a couple of problems. 1. A block on a spring is pulled to the right and released at t= 0s. It passes x = 3.0 cm at t= 0.685s, and it passes x= -3.0 cm at t= 0.886s. What is the angular frequency? What is the amplitude? I know what equatios I need to use, but without...
  6. P

    Simple harmonic motion for block of mass

    the problem gives x(t)= A cos( (k/m)^(1/2) * t) A block of mass m is attached to a spring whose spring constant is k. The other end of the spring is fixed so that when the spring is unstretched, the mass is located at x=0. View Figure . Assume that the +x direction is to the right. The...
  7. A

    How Do You Calculate the Phase Constant in Simple Harmonic Motion?

    An air-track glider attached to a spring oscillates with a period of 1.50 seconds At t=0 the glider is 5.40 cm* left of the equilibrium position and moving to the right at 39.2*cm/s. What is the phase constant , if the equation of the oscillator is taken to be x=A*cos(wt+Fi original) ...
  8. S

    Energy and Simple Harmonic Motion

    In preparation for shooting a ball in a pinball machine, a spring (k = 675 N/m) is compressed by 0.0690 m relative to its unstrained length. The ball (m = 0.0540 kg) is at rest against the spring at point A. When the spring is released, the ball slides (without rolling) to point B, which is...
  9. S

    Trouble with Simple Harmonic Motion

    I am having trouble with this question: 1. A particle oscillating in simple harmonic motion is: in equilibrium at the center of its path because the acceleration is zero there or in equilibrium at the ends of its path because the acceleration is zero there 2. When a body...
  10. F

    Simple Harmonic Motion - Period of a Pendulum

    We are talking about SHO in physics and the forumula for period T of a pendulum was introduced - T=2*pi*(L/g)^.5 where L is the length of the pendulum arm/string and g is acceleration due to gravity. the instructor also said this was an approximation that was only accurate for small angles...
  11. P

    What Is the Smallest Value of Time t for This Simple Harmonic Motion?

    Hi, I've been stuck on trying to figure out what I am not seeing in the problem as i just can't seem to get the answer. A particle moving in simple harmonic motion with a period T = 1.5s passes through the equilibrium point at time t initial = 0 with a velocity of 1.0m/s to the right. At...
  12. K

    How Do You Solve These Harmonic Motion Problems?

    please help me with these two problems: 1. A meter stick is hung at its center from a thin wire It is twisted and oscillates with a period of 6.06 s. The meter stick is sawed off to a length of 72.4 cm. This piece is again balanced at its center and set in oscillation. With what period does...
  13. N

    Simple Harmonic Motion Tuning Fork Question

    Q: A tuning fork vibrates at a frequency of 264 Hz and the tip of each prong moves 1.66 mm to either side of center. Calculate the maximum speed of the tip of a prong. So far I've found that Vmax = omega*A, but I don't know how to find A. Am I going in the wrong direction? Or is there a way...
  14. H

    Simple harmonic motion pinball problem

    I have been looking at this problem forever. It is probably easy, but I am making it harder. States: In preparation for shooting a ball in a pinball machine, a spring (k=675 N/m) is compressed by 0.0650m relative to its unstrained length. The ball ( m=0.0585kg) is at rest against the spring at...
  15. I

    Simple Harmonic Motion and free-fall accelerations

    A "seconds" pendulum is one that goes through its equilibrium position once each second. (The period of the pendulum is 2.000 s.) The length of a seconds pendulum is 0.9927 m at Tokyo and 0.9942 m at Cambridge, England. What is the ratio of the free-fall accelerations at these two locations...
  16. C

    Simple Harmonic motion and collisions

    A block of mass 2kg oscillates on the end of a spring in SHM with a period of 20ms. The position of the block is given by: x=(1.0cm)cos(wt+2pi). Another block of mass 4kg slides toward the oscillating block with velocity of 6m/s. The two blocks undergo a completely inelatic collision at time...
  17. N

    Simple Harmonic motion problems

    http://sweb.uky.edu/~lsadam0/problem2.JPG Im kinda lost on this problem. Shouldnt the Y motion be described as A*sin(wt)? In there equation we are considering when x=0, so the kx term is removed, but where is this third term coming from, and then should Y motion just be described as...
  18. J

    Simple harmonic motion object problem

    I have this problem: An object is undergoing simple harmonic motion with period 0.330 s and amplitude 5.95 cm. At t=0 the object is instantaneously at rest at x= 5.95 cm. i need to find : the time it takes the object to go from x= 5.95 cm to x= −1.49 cm. I have tried using x = A cos(wt +...
  19. A

    Simple harmonic motion glider problem

    An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t = 0 s . It then oscillates with a period of 2.40 s and a maximum speed of 46.0 cm/s. What is the amplitude of the oscillation? i tryed solving for t by using the equation x(t) = A cos...
  20. U

    Simple Harmonic Motion of a Mass on a Spring

    A 2 kg mass is attached to a spring aand placed on a horizontal, smooth surface. A force of 20N is required to hold the mass at reast when it is pulled .200m from the equilibrium position. The mass is released and undergoes simple harmoic motion. a) what is the force constant? b) frequency...
  21. K

    How Do Damping Constants Affect Amplitude in Simple Harmonic Motion?

    Urgent! Damped Simple Harmonic Oscillation The thread topic says 2 masses, but there is actually only one! I'm not asking for the complete solution for this problem; I simply just don't know WHERE to start... The question is as follows: In Figure 15-15, a damped simple harmonic oscillator...
  22. U

    Simple harmonic motion of a ball drop

    a ball is dropped from a heright of 4m and makes a perfectly elastic collision with the ground. Assuming that no energy is lost due to air resistance, a) show that the motion is periodic b) determine the period of the motion c) is the motion simple harmonic? a) I know that periodic...
  23. K

    Exploring Harmonic Motion and Strobe Phenomenon

    Harmonic motion is when an object pretty much goes back and forth, right? Also, what does the word 'strobe' mean? I once heard a member here say that if our eyes worked like a camera and took a picture 60 times a second that a light that flashed 61 times per second would appear to strobe at...
  24. D

    Simple Harmonic Motion Question

    I am going brain dead on a rather simple question. Appreciate some help. A mass of 4.5 KG attatched to a horizontal spring of constan 75 KN/m is compressed 0.4 m from Equilibirium and then a loose mass of 2.5 KG is placed in front of it . IF the mass is now released: 1. at what point...
  25. maverick280857

    Simple Harmonic Motion of a Dielectric Slab in a Parallel Plate Capacitor

    Hello Here's a situation I would like to discuss... Suppose we have an ideal parallel plate capacitor which is filled with air (or vacuum) with permittivity = 1. Now if a dielectric slab of width equal to the space (d) between the plates is inserted into the space between the plates, it...
  26. S

    Please help with Simple Harmonic motion

    Ok the system which is doing the oscillations is described here http://scienceworld.wolfram.com/physics/SpringsTwoSpringsandaMass.html however, that differential equation over there gives the equation of motion. What i need is the differential equation for the position of the mass ALso...
  27. F

    Simple harmonic motion problem

    i need help... A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 1.0 J of work is required to compress the spring by 0.15 m. If the mass is released from rest with the spring compressed, it experiences a maximum...
  28. S

    Question regarding simple harmonic motion

    I have my solution and my doubt in the attachment that followed.
  29. W

    A physics question with simple harmonic motion

    This is a little question that I am not sure how to do because of the way gravity works with vertical springs. A 3 lb block rests on top of a 5 lb block which is attacked to a k=1000 N/m spring force spring following hooke's law. The blocks are released and allowed to reach equilibrium (.08...
  30. B

    Simple Harmonic Motion of a horizontal spring

    A 1.00-kg object is attached to a horizontal spring. The spring is initially stretched by 0.100 m, and the object is released from rest there. It proceeds to move without friction. The next time the speed of the object is zero is 0.500 s later. What is the maximum speed of the object? I...
  31. N

    Simple harmonic motion and time

    A particle moving along the x-axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 1.70 cm and the frequency is 2.00 Hz. Determine the total distance traveled between t = 0 and t = 0.75 s. how would...
  32. B

    Simple Harmonic Motion of a car's tires

    While riding behind a car traveling at 3.00 m/s, you notice that one of the car's tires has a small hemispherical bump on it's rim. If the radii of the car's tires are .300 m, what is the bump's period of oscillation? Can anyone tell me where to start with this? I'm actually not even sure...
  33. S

    Maximizing Speed in Simple Harmonic Motion: Solving for Displacement

    An object attached to a spring (k = 30 N/m) has a velocity of 2.5 m/s when it is .55 m from equilibrium, and has a period of 2.45 s. After doing other parts I found the mass to be 4.561 kg, the total energy of the system to be 18.79 J, the amplitude to be 1.12 m, and the maximum speed to be...
  34. C

    Simple Harmonic motion of particle on a table

    1. A particle mass attached to one end of a light spring is executing SHM on a smooth horizontal table. If another identical particle is attached to the other end of the spring, what is the period of oscillation? I don't know how to figure this problem out...I used to deal with a spring fixed...
  35. S

    Simple harmonic motion mass on a spring

    A mass is on a spring is pulled down and released.Show thatit performs simple harmonic motion. as the mass is pulled down and released restoring force pulls it upwards but as it reaches on the top extreme the gravity pulls it down n continuous to oscillate.but how does it prove that motion is...
  36. S

    Hooke's Law and Simple Harmonic Motion

    We did an experiment with a vertical spring-mass system. Here is an example of data collected: Mass------------T (period) 200 g-----------.3 s 400g------------.5 s My question is why does the period increase as the mass increases? I know that the amp. and T are independent of each...
  37. J

    Help Solving Harmonic Motion Problem

    Can you offer some help on the following question? I've been trying different things for a while but can't get the right answer. Thanks! At time t = 0, consider a 1/2 wavelength long section of the rope which is carrying the wave y = 0.06 cos(2.1 t - 2.4 x) between two points which have zero...
  38. S

    Simple harmonic motion problem

    In a block-spring system with a block of mass m and a spring of spring constant k, prove that the angular velocity ω of the block = (k/m)^(1/2). I can prove this easily in the following manner: F = ma Newton's law F = -kx Hooke's law a = -ω^2x ma = -kx = -mω^2x k = mω^2 ω^2 = (k/m)...
  39. P

    Period of Simple Harmonic Motion: Amplitude Independence

    Why is the formula for period of simple harmonic motion independent of amplitude?
  40. D

    Displacement in simple harmonic motion

    i have a problem i am working on and i am just not sure how to do it i was looking for some help i will state the problem then explain the way i am trying to do it. thanks for any help in advance. A 0.27 kg mass is suspended on a spring that stretches a distance of 4.9 cm. The mass is then...
  41. E

    What is realy the idea of damped simple harmonic motion?

    i am finding damped SHM difficult to understand can anyone give sugestion as to what coul .do
  42. Q

    Block on piston undergoing simple harmonic motion

    A block rides on a piston that is moving vertically with simple harmonic motion. if the shm has period 1 s at what amplitude of maotion will the block and piston seperate? T= 1 / f 1= 1 / f x= x cos (wt+0) x= x cos( 2 * pi * 1 + 0) where can i go from here?
  43. P

    Diving board oscillates with simple harmonic motion

    A diving board oscillates with simple harmonic motion of frequency 3.6 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there will not lose contact with the board during the oscillation?
  44. S

    How Do You Derive Equations for Position and Velocity in Simple Harmonic Motion?

    I am confused by the following problem. Any help / hints would be greatly appreciated! I understand that the velocity equation is the derivative of the position function... i just don't understand how to derive these first / last equations. :bugeye: THANKS! The initial position and...
  45. S

    Mass connected to two springs - simple harmonic motion

    A mass m is connected to two springs, with spring constants k1 and k2. (m connected to k2, which is connected to k1 which is connected to a wall horizontally). Show that the period for the configuration is given by T = 2 \pi \sqrt{m ( k^{-1}_1 + k^{-1}_2)} Well I know .5kA^2 = .5mv^2...
  46. L

    Solving for Phi in Harmonic Motion Equation

    A spring with spring constant 190 N/m vibrates with an amplitude of 8.0 cm when 0.380 kg hangs from it. What is the equation describing this motion as a function of time? Assume the mass passes through the equilibrium point, toward positive x (upward), at t = 0.100 s. x=A*cos(omega*t +...
  47. C

    2kg ball in simple harmonic motion

    a 2-kg ball is supended from a spring. when disturbed in a vertical direction, the ball moves up and down in simple harmonic motion with a period of 0.25s. a. what is the upward force exerted on the ball by the spring when the ball is at the midpoint of its up-and-down path? b. how much...
  48. S

    Confused (simple harmonic motion problem)

    Ok I've been trying this problem : ---A 21.0kg block at rest on a horizontal frictionless table is connected to the wall via a spring with a spring constant k=14.0N/m. A 2.10×10-2kg bullet traveling with a speed of 530m/s embeds itself in the block. What is the amplitude of the resulting...
  49. S

    Simple Harmonic Motion of a spring and hammer

    What seems to be a very simple question is confusing me. ----At t = 0, a 790g mass at rest on the end of a horizontal spring (k = 101N/m) is struck by a hammer, which gives it an initial speed of 2.66m/s. Determine the amplitude.----- I know that the amplitude is the 'maximum excursion...
  50. J

    Simple harmonic motion (4 questions)

    1. A 4.0kg block is suspended from a spring with force constant of 500N/m. A 50g bullet is fired into the block from directly below with a speed of 150m/s and is imbedded in the bloack. (a) Find the amplitude of the resulting simple harmonic motion. (b) What fraction of the original kinetic...
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