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. N

    Simple Harmonic Motion and spring displacement

    Homework Statement An object of mass m is suspended from a vertical spring of force constant 1800 N/m. When the object is pulled down 2.50 cm from equilibrium and released from rest, the object oscillates at 5.500 Hz. a) Find m, b) Find the amount the spring is stretched from its unstressed...
  2. C

    Simple Harmonic Motion on a moving platform

    I had my physics midterm today and I totally blanked out. I want to know how to solve it for next time. So In the picture, there are two springs connected to the mass on a platform. a) if the platform is at rest, find the angular frequency the expression for angular frequency is...
  3. J

    Oscillating in Simple Harmonic Motion?

    Homework Statement A 200-g object is oscillating in simple harmonic monition with an amplitude of 2 cm and a period of 0.4 seconds. Find the velocity when its displacement from the equilibrium position is 0.5 cm. Homework Equations Restoring Force = -(constant force)(displacement)...
  4. S

    Simple Harmonic Motion problem

    Homework Statement An elastic string is attached to A on a horizontal plane and a mass is attached to the other side of the rope.Then the rope is pulled to C and release.It engage in SHM from C to B and D to E and so on natural length = l extension = a max end points = E & C...
  5. H

    Simple Harmonic Motion: Position, Velocity, & Acceleration

    Homework Statement A 1.00-kg glider attached to a spring with a force constant 49.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is released from rest at x = -3.50 cm (that is, the spring is compressed by 3.50 cm). Find the position, velocity, and...
  6. M

    An object is undergoing simple harmonic motion

    Homework Statement An object is undergoing simple harmonic motion with period 1.190 and amplitude 0.640 At t=0 the object is at x=0 . How far is the object from the equilibrium position at time 0.475 ? Homework Equations The Attempt at a Solution x=Acos(ωt+∅) x=...
  7. M

    Calculating Time for Simple Harmonic Motion

    Homework Statement An object is undergoing simple harmonic motion with frequency = 3.2 Hz and amplitude = 0.12 m. At = 0 the object is at = 0. How long does it take the object to go from = 0 to = 7.2×10−2 m? Homework Equations The Attempt at a Solution s(t)=Asin(ωt)...
  8. M

    Simple Harmonic Motion find Mass

    Homework Statement A block is attached to a horizontal spring with k = 75 N/m undergoes SHM with an amplitude of 0.15m. If the speed of the block is 1.7 m/s when the displacement is 0.12m from equilibrium, what is the mass of the block?Homework Equations E = E' E_{k} = \frac{1}{2}mv^{2} E_{s} =...
  9. M

    Simple Harmonic Motion and Springs

    An object of mass m is supended from a vertical spring of force constant 1269 N/m. When the object is pulled down 0.068 m from equilibrium and released from rest, the object oscillates at 10 Hz. The mass of the object is ____ kg. τ= 2∏*sqrt(M/K) M = mass K = spring constant 1/f = τ...
  10. C

    A mass between two springs-simple harmonic motion

    Homework Statement A 4kg mass remains at rest on a friction free surface due to equal and opposite pulls of two springs. Spring 1 is stretched 4 meters. The k in spring 1 equals 40 N/m and the k in spring 2 equals 60 N/m. This is what the the picture looks like in words. From left to the...
  11. C

    Very easy simple harmonic motion question that I keep getting wrong

    Homework Statement In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the following expression, where x is in centimeters and t is in seconds. x = (7.00 cm) cos(4t + π/6) At t = 0, what is its velocity? Homework Equations v(t)...
  12. J

    Calculating Velocity in Simple Harmonic Motion: A Pendulum Clock Analogy

    Homework Statement Speed of particle executing simple harmonic motion with amplitude A is half of the maximum speed. At that instant, displacement of the particle is ? Homework Equations The Attempt at a Solution
  13. O

    Simple Harmonic Motion - basic question

    A mass on a spring undergoes simple harmonic motion with amplitude A. a) In a time equal to three periods, what is the magnitude of the displacement of the mass? b) In a time equal to three periods, what actual distance did it travel? In the first part, I was at first trying to use an...
  14. D

    Understanding Forced Harmonic Motion in a Pendulum System

    I have a pendulum swinging with frequency w in a frictionless environment and I apply a periodic harmonic driving force also at frequency w but out of phase with the swinging pendulum. What happens exactly? Does the driving force bring the pendulum into phase with the force and then we see the...
  15. M

    Finding Velocity in Simple Harmonic Motion

    The position of a particle is given by x = (6.6)cos(4.1t) where t is in seconds. The frequency of the particle's oscillation is ____ Hz. I am completely at lost for this, its a new chapter in ap physics, and i don't understand it at all, my teacher is really busy so can someone explain...
  16. 4

    Exploring Factors Affecting Simple Harmonic Motion in a U-Tube

    Homework Statement These questions are regarding water undergoing SHM in a u-tube. Q1) What is the effect on the time period and damping in a u-tube when using oil instead of water? Q2) What is the effect on the time period if the liquid (inside the u tube) is heated? Q3) How can...
  17. V

    Simple Harmonic Motion displacement

    Homework Statement A mass m is attached to a horizontal spring of spring constant k. The spring oscillates in simple harmonic motion with amplitude A. Answer the following in terms of A. At what displacement from equilibrium is the speed half of the maximum value? Homework Equations PE1 +...
  18. K

    Simple harmonic motion problem

    A mass between 2 springs moves with shm. it oscillates between 2 points 5cm apart and completes 40 oscillations in 1min whats its max speed? Please help i always get the wrong answer The answer is 0.44 but why?
  19. G

    Simple Harmonic Motion with Spring

    Homework Statement A massless spring is hanging vertically. With no load on the spring, it has a length of 0.22 m. When a mass of 0.68 kg is hung on it, the equilibrium length is 0.75 m. At t=0, the mass (which is at the equilibrium point) is given a velocity of 4.88 m/s downward. At...
  20. Q_Goest

    Impressive harmonic motion demonstration

    The YouTube video here will get you to think a bit. Basically, 15 separate pendulums that create various patterns: I wonder though if you could say how many given patterns are created. Not sure how to describe that... what do you think?
  21. N

    Harmonic motion with a spring question

    A 0.1-kg mass is attached to a spring having a spring constant 3.6 kg/s^2. The system is allowed to come to rest. Then the mass is given a sharp tap, imparting an instantaneous downward velocity of 0.4 m/s. If there is no damping present, find the amplitude A and frequency ω of the resulting...
  22. C

    Simple Harmonic Motion with Impulse

    Homework Statement A particle P of mass 0.6kg is attached to one end of a light elastic spring of modulus of elasticity 72N and natural length 1.2m. The other end of the spring is fixed to a point A on the smooth horizontal table on which P rests. Initially P is at rest and is 1.2m from A...
  23. G

    Simple Harmonic Motion conceptual question

    Homework Statement Answer the following questions for a mass that is hanging on a spring and oscillating up and down with simple harmonic motion. Note: the oscillation is small enough that the spring stays stretched beyond its rest length the entire time. Answers available: Top, Equilibrium...
  24. FeDeX_LaTeX

    Damped and Forced Harmonic Motion

    Homework Statement http://desmond.imageshack.us/Himg812/scaled.php?server=812&filename=quesq.jpg&res=medium Homework Equations F = ma, F = -kx, SHM equations The Attempt at a Solution Here's the diagram they've done for part (b)...
  25. B

    Simple harmonic motion problem.

    Homework Statement A 10.0-g bullet is fired into and embeds in a 2.00-kg block attached to a spring with a spring constant of 19.6 N/m and whose mass is negligible. How far is the spring compressed if the bullet has a speed of 300 m/s just before it strikes the block, and the block slides on a...
  26. R

    Reference frame for harmonic motion.

    If you a mass being accelerated by a force which is acting upon a spring attached to the mass it will exhibit harmonic motion. However unlike a fixed harmonic oscillator there is no explicit solution to the equation which describes the motion of the mass in a reference frame outside of the...
  27. H

    Understanding Simple Harmonic Motion and its Equations | Physics Explained

    Simple Harmonic Motion!? Hi All, New to the forum, sorry if this is a thread that has been discussed before, however I've had a quick look and have been killing myself for days over this. Approached my college tutor today and he couldn't explain it!? I'm almost sure that it is something...
  28. T

    Spring System in Harmonic Motion. How do I find

    Homework Statement A .5kg mass is suspended from a spring. A student attaches a second mass, .24kg, to the bottom of the first mass using tape (neglect the mass of the tape and spring). The spring extends an aditional 2cm when the second mass is attached. a) Find the period of the...
  29. F

    Simple Harmonic Motion + Regular Kinematics

    Homework Statement A particle moves along the x axis. It is initially at the position 0.250 m, moving with velocity 0.200 m/s and acceleration -0.290 m/s2. Suppose it moves with constant acceleration for 5.80 s. Position of Particle after 5.80 Seconds - -3.4678 m. Velocity of Particle...
  30. C

    Simple harmonic motion: time for maximum speed

    Homework Statement 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 3.20 cm, and the frequency is 1.40 Hz. Determine the maximum speed of the particle. Determine the...
  31. S

    Derivation: Simple Harmonic Motion

    I know how to arrive at a = -(k/m)x for a SHM system. However, most derivations i found did an unexplained step from here onward. They simply let k/m = ω2. And later on then mention ω as the angular frequency and link to the period of oscillation. My question is, Why did...
  32. nukeman

    Simple Harmonic Motion Problem - Need help Thanks

    Homework Statement Below is the image of the question I am having trouble with. B) and C) I need help with! Homework Equations The Attempt at a Solution Can anyone point me in the right direction? B and C are my trouble questions. I don't know how to prove that the...
  33. J

    Simple Harmonic Motion amplitude

    Homework Statement An object in SHM oscillates with a period of 4.0 s and an amplitude of 10 cm. How long does the object take to move from x = 0.0 cm to x = 6.0 cm? Homework Equations T = 2*pi/w x(t) = Acos(wt) or x(t) = Asin(wt) The Attempt at a Solution T = 4.0 s A = 0.10...
  34. nukeman

    Can someone please explain this simple harmonic motion equation for me?

    Homework Statement This is not a homework question, as we just started getting into SHM, and I want to be 100% clear what this equation means. Can someone please all the parts, or have a site that really explains this formula? Homework Equations The Attempt at a Solution
  35. G

    Simple Harmonic Motion question.

    Homework Statement Two simple pendulums of length 0.40 m and 0.60 m are set off oscillating in step. Calculate (a) after what further time the two pendulums will once again be in step, (b) the number of oscillations made by each pendulum during this time. (Assume g = 10 ms-2Homework Equations...
  36. J

    Deriving equation of simple harmonic motion

    Derivation of simple harmonic motion I'm looking at the wikipedia page for simple harmonic motion (http://en.wikipedia.org/wiki/Simple_harmonic_motion) and I'm confused by this line: c_1cos(\omega t) + c_2sin(\omega t)=A*cos(\omega t - \phi) How did they get from the left hand side to the right...
  37. G

    Simple Harmonic Motion question.

    Homework Statement We say that the equation a= ω2x defines simple harmonic motion - it tells us what is required if a body is to perform s.h.m. The equation x= xosinωt is then described as a solution to the equation, since it tells us how the displacement of the body varies with time. If you...
  38. M

    Finding the phase angle for simple harmonic motion

    Homework Statement A .25 kg block oscillates on the end of a spring with a force constant of 200 N/m. If the oscillation started by elongating the spring 0.15 m and giving the block a speed of 3 m/s, (a) what is the amplitude of the oscillation, and (b) If the clock is started when the block...
  39. G

    Simple Harmonic Motion question.

    Homework Statement Explain why the motion of someone jumping up and down on a trampoline is not simple harmonic motion. (Their feet lose contact with the trampoline during each bounce.) 2. The attempt at a solution I really can't think of anything. Maybe I haven't completely...
  40. M

    Finding the amplitude in simple harmonic motion

    Homework Statement Consider a block-spring system that forms a linear simple harmonic oscillator, with the block undergoing SHM. The angular frequency is 9.78 rad/s, the frequency is 1.6 Hz and the period is 640 msec. The block is pulled from its equilibrium position at x=0 (at time = 0) to...
  41. Y

    Simple Harmonic Motion (displacement function)

    Homework Statement I learned that in simple harmonic motion, the displacement fuction is x(t) = A sin(ωt + Φ) or x(t) = A cos(ωt + Φ) but when do you use sine function or cosine function? can I use whatever I want whether a sine or cosine function? And what's that Φ in...
  42. B

    Another simple harmonic motion problem

    Homework Statement An object is undergoing SHM with period 0.9 s and amplitude 0.32 m. At t=0, the object is at x=0.32 m and is instantaneously at rest. Calculate the time it takes the object to go from 0.32 m to 0.16 m, and to go from 0.16m to 0 m. Homework Equations x=Acos(wt+θ)...
  43. B

    Simple Harmonic Motion Problem Help

    a 2.00 kg frictionless block is attached to an ideal spring with force constant 300 N/m. at t=0 the spring is neither stretched nor compressed and the block is moving in the negative direction at 12.0 m/s. Find the amplitude, the phase angle, and write and equation for the position as a...
  44. J

    Lab Problems with Simple Harmonic Motion in Springs

    Homework Statement During lab we measured the amount a spring was stretched when various masses where hung on it to verify Hooke's Law. We started with a 50 gram mass and then increased with 50 grams up until 350, for seven measurements. We then graphed the force and displacement. The lab...
  45. A

    Solving Simple Harmonic Motion Question

    I am having a question and tries to solve a problem for days. Consider general SHM. When the particle reaches to the maximum displacement, a if a velocity U is given to the particle towards to the center of SHM, (keeping the same force mω^2x) 1. What would happen to the SHM...is it same or...
  46. A

    Solving Simple Harmonic Motion Question

    I am having a question and tries to solve a problem for days. Consider general SHM. When the particle reaches to the maximum displacement, a if a velocity U is given to the particle towards to the center of SHM, (keeping the same force mω^2x) 1. What would happen to the SHM...is it same or...
  47. E

    Simple harmonic motion finding velocity trouble

    Homework Statement A block with mass m =6.6 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.26 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.4 m/s. The block oscillates on the spring without...
  48. T

    Calculating Velocity in Simple Harmonic Motion

    Homework Statement The position of a 49 g oscillating mass is given by x(t)= (2.3cm) cos 11t , where t is in seconds. Determine the velocity at t = 0.43s Where: f= 1.75 t=0.43s vmax=0.25 m/s Homework Equations I'm using v(t)= -vmax sin (2pi*f*t) The Attempt at a Solution Using above...
  49. V

    Standard Harmonic Motion of a Plate

    A child with poor table manners is sliding his 240 dinner plate back and forth in SHM with an amplitude of 0.120 on a horizontal surface. At a point a distance 7.00×10−2 away from equilibrium, the speed of the plate is 0.370 . (a) What is the period (b)What is the displacement when the speed...
  50. W

    Simple harmonic motion and central forces.

    Homework Statement Assuming Earth to be a solid sphere, show that if a straight hole were drilled from pole to pole that a particel dropped would undergo simple harmonic motion. Show that the period of the oscillation depends only on the Earth's density and is independent of size. What is...
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