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. K

    Simple Harmonic Motion Homework: Finding Velocity, Time, and Constant Values

    Homework Statement Natural length is "l" and when a "m" mass is hanged on the P edge, it dragged by another "L" length. Point "O" is "4L" far from the floor. 1. Find \lambda 2. The mass will be hold at point "O" and released with the starting velocity √(gL). Find the velocity of the mass after...
  2. N

    Simple Harmonic Motion, spring periods

    Hi guys! I'd really like help with this as I'm stuck. Homework Statement Investigate the mathmatical relationship between period of a spring and mass. Finding the spring constant (k) from measuring periods with a spring and different hanging masses. Homework Equations T = 2pi...
  3. S

    Simple Harmonic Motion Question

    Homework Statement A particle moves with SHM in a straight line. In the first second after starting from rest,it travels a distance of 1m in a constant direction. In the next second, it travels a distance of 2m in the same direction. Find its maximum acceleration Homework Equations...
  4. R

    Damped Simple Harmonic Motion: Solving for Period and Phase Delta

    Homework Statement http://img534.imageshack.us/img534/6503/questiono.jpg Homework Equations The Attempt at a Solution (a) I'm not sure how to approach this part. I appreciate any help to get me started. (b) I know that the period of oscillation is given by T'=\frac{2 \pi}{\omega '} I...
  5. G

    Simple Harmonic Motion and Resonance

    Homework Statement A car with mass 1220kg including the driver travels over a bridge with expansion gaps spaced 5.5m apart. At a speed of 12.0m/s, the car bounces up and down with exceptionally large amplitude. Two more 80kg passengers now get in the car. a) What speed will result in maximum...
  6. 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...
  7. 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...
  8. J

    Oscillating in Simple Harmonic Motion?

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  9. S

    Simple Harmonic Motion problem

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  10. 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...
  11. 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=...
  12. 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)...
  13. 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} =...
  14. 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...
  15. 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)...
  16. 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...
  17. 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...
  18. 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...
  19. 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 +...
  20. 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?
  21. 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...
  22. C

    Simple Harmonic Motion with Impulse

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  23. G

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  24. 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...
  25. H

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  26. F

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  27. C

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  28. S

    Derivation: Simple Harmonic Motion

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  29. 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...
  30. 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...
  31. 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
  32. 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...
  33. 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...
  34. 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...
  35. 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...
  36. 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...
  37. 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...
  38. 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...
  39. 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)...
  40. 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...
  41. 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...
  42. 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...
  43. 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...
  44. 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...
  45. E

    Simple harmonic motion question

    Homework Statement An object undergoing SHM with a period 0.9s and amplitude of 0.32 m at t=0 the object is at 0.32 m and is instantaneously at rest. Calculate the time it takes the object to go a) from 0.32 to 0.16 m b) from 0.16 m to 0 i can do a but don't understand why when i do the...
  46. D

    Simple Harmonic Motion - Mass and massive spring

    Homework Statement A block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a horizontal, frictionless track (Figure P15.62). The force constant of the spring is k and the equilibrium length is l. Assume that all portions of the spring oscillate in...
  47. D

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    Homework Statement Okay, so we've got a solid cylinder attached to a horizontal massless spring that rolls without slipping along a horizontal surface. The system is released from rest with the spring stretched past the equilibrium point. (The first two parts of this problem ask for...
  48. 0

    Simple Harmonic Motion Problems

    I am having a hard time solving for k in the equation T = 2 x pi sq. rt. (m/k) I know this is simple algebra but its keeping me from solving this.
  49. T

    Energy and Simple Harmonic Motion of spring

    Homework Statement A 2.00-kg object is hanging from the end of a vertical spring. The spring constant is 50.0 N/m. The object is pulled 0.200m downward and released from rest. Complete the table below by calculating the translational kinetic energy, the gravitational potential energy, the...
  50. A

    What is the connection between simple harmonic motion and pendulum motion?

    Homework Statement What is the connection between simple harmonic motion and pendulum motion? Homework Equations Harmonic motion period=T=2piroot(m/k) Pendulum motion period=T=2piroot(L/g) The Attempt at a Solution Conservation of momentum?? Thanks for any help!
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