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. F

    Simple Harmonic Motion: Fire Net Stretch Calculations

    Simple harmonic motion! :( Homework Statement A 65-kg person jumps from a window to a fire net 18m below, which stretches the net 1.1m. Assume that the net behaves like a simple spring, and (a) calculate how much it would stretch if the same person were lying in it. (b) How much would it...
  2. K

    Simple Harmonic Motion confusion

    [b]1. A 14.7g mass is attached to a frictionless horizontal spring. After the spring was stretched a certain distance and released, its maximum speed was found to be 4.22 m/s. If the speed at x = -2.84 cm is 1.63 m/s, what is the frequency of the oscillating spring? [b]2. PEe = kx^2/2 E=KE...
  3. S

    Simple Harmonic Motion Question.

    Homework Statement When a mass is hung from a spring, the spring elongates by 10.6cm. What will the period of the resulting oscillations be if the mass is displaced from equilibrium? Homework Equations T=2(pi)\sqrt{m/k} The Attempt at a Solution I have no clue what do with this...
  4. A

    Electric Dipole in Simple Harmonic Motion

    Homework Statement An electric dipole in a uniform horizontal electric field is displaced slightly from its equilibrium position, where theta is small. The separation of the charges is 2a, and each of the two particles has mass m. Assuming the dipole is released from this position, show that...
  5. M

    Simple harmonic motion problem, finding velocity as a function of position

    Homework Statement I need help finding velocity as a function of position, the t in the argument of tan, causes a problem for me when integrating. can someone help, maybe my approach is completely off, i am trying to fing the unknown phi, knowing the velocity and acceletation when position...
  6. J

    Springs and simple harmonic motion

    Homework Statement A mass is oscillating on a spring with a period of 1.45 s. At t = 0 the mass has zero speed and is at x = 8.80 cm. What is the magnitude of the acceleration at t = 2.30 s? Homework Equations x(t)=Acos(wt + phi) a(t)=-Aw^2cos(wt + phi) a=w^2x T=2pi/w The Attempt...
  7. J

    Solving Simple Harmonic Motion for All Time

    Homework Statement I have that a oscillating mass undergoes shm. It is accelerated (forced oscillation) by 1ms^-2, for time pi/2 as it goes through the origin and then accelerated by -1ms^-2 for another time pi/2, then it is at the origin after the second acceleration. I need to determine...
  8. C

    Effect of Breaking Mass on SHM Time Period & Amplitude

    Could anybody temme what wuld happen to the time period and the amplitude of oscillations if a mass attaching to a ruler, lying horizontally on the table, is broken ...then what effect would this have on the amplitude and time period of oscillations? I say that amplitude would increase...
  9. T

    Simple Harmonic Motion Question Advise required please

    Simple Harmonic Motion Question... Advise required please! A vehicle engine has a stroke of 180mm. The motion of the piston is simple harmonic. calculate max linear velocity and acceleration at 4200rpm? Calculate max force to the crankshaft if the piston has an effictive mass of .35kg at an...
  10. T

    Simple harmonic motion rise and fall of water

    Homework Statement The rise and fall of water in a harbour is simple harmonic. The depth of water varies between 5.0 m at low tide and 9.0 m at high tide. The time between sucessive low tides is 12 hours. A ship, which requires a minimum depth of 6.0 m approaches the harbour at low tide, how...
  11. A

    Solving Simple Harmonic Motion: Cart Position and Time Comparison

    Homework Statement The position of a an air-track cart that is oscillating on a spring is given by (12.5cm)cos[(18.0s-1)t]. At what value t after t=0 is the cart first located at x=12.2 cm? The Attempt at a Solution 12.2 cm = (12.5cm)cos[(18.0s^-1)t]. How do I factor t out? Thanks
  12. P

    Simple Harmonic Motion and equilibrium

    Homework Statement A 100-g block hangs from a spring with k = 5.2 N/m. At t = 0 s, the block is .20 m below the equilibrium position and moving upward with a speed of 2.10 m/s. What is the block's speed when the displacement from equilibrium is .324 m? Homework Equations w0=sqrt(k/m)...
  13. G

    Simple Harmonic Motion pulsatance Question

    Homework Statement A particle oscillates with an s.h.m of amplitude 50mm and a maximum speed of 0.25 m/s. Calculate the pulsatance, period and maximum acceleration Homework Equations x = a sin(wt) dx/dt=awcos(wt) d2x/dt2=aw^2sin(wt) Put in x=0.05sin(wt) 0.25=0.05wcos(wt)...
  14. W

    Simple Harmonic Motion of a hanging spring

    Homework Statement A 450 g object oscillates from a vertically hanging light spring once every .55 s. The object is released with the spring compressed by 10 cm from the equilibrium position. What is the velocity of the object 3.00 s after it is released? Homework Equations...
  15. I

    Calculating Spring Constant and Properties of Simple Harmonic Motion

    Homework Statement A vertical spring, fixed at the upper end, has a mass attached to the lower end. When the spring is given a small extension it was observed to oscillate at a rate of 45 cycles per minute. When an additional 160g mass is attached to the spring, it oscillated at a rate of...
  16. P

    Simple harmonic motion of an ideal spring

    simple harmonic motion ! Homework Statement An ideal spring has a spring constant k=25N/M and is suspended vertically. A 1kg object is attatched to the unstrechted spring and released. It then performs ocillations. What is the magnitude of the acceleration of the body when the extension of...
  17. V

    Simple Harmonic Motion Questions

    Simple Harmonic Motion Questions-springs Homework Statement A .20 kg mass is sliding on a horizontal frictionless air track with a speed of 3 m/s when it instantaneously hits and sticks to a 1.3 kg mass initially at rest on the track. The 1.3 kg mass is connected to one end of a massless...
  18. P

    Simple harmonic motion problem

    Homework Statement An ideal spring has a spring constant k=25N/M and is suspended vertically. A 1kg object is attatched to the unstrechted spring and released. It then performs ocillations. What is the magnitude of the acceleration of the body when the extension of the spring is at maximum...
  19. W

    Simple Harmonic Motion Acceleration Calculation and Equations

    Homework Statement I have been stuck on this question for quite some time. I'm trying to study for the test and actually have the answer, but I can't figure it out. The answer is 1.3X10-6cm/s2 The following graph represents an object oscillating in simple harmonic motion. What is the...
  20. 3

    Particle Simple harmonic motion particle problem

    Homework Statement For a particle in simple harmonic motion, show that vmax = (pi/2) vaverage, where vaverage is the average speed during one cycle of the motion. Homework Equations v(t) = -vmaxsin(wt + phi) vmax = 2piA/ T = wA The Attempt at a Solution I'm really not sure at...
  21. K

    Finding Restoring Force for Simple Harmonic Motion: 700g Cylinder in Water

    Homework Statement a 700 g cylinder of base area a=30 cm^2 and height 40 cm is floating upright in water. A 50 g mass, resting on top of the cylinder is suddenly removed. find the restoring force. Homework Equations The Attempt at a Solution
  22. R

    Maximum velocity for a piston in simple harmonic motion.

    Homework Statement A piston in an automobile engine is in simple harmonic motion. Its amplitude of oscillation from the equilibrium (centered) position is ±6.87 cm and its mass is 1.472 kg. Find the maximum velocity of the piston when the auto engine is running at the rate of 3220...
  23. T

    Euler's Equations / Simple Harmonic Motion - please check

    Homework Statement [PLAIN]http://img819.imageshack.us/img819/4509/mectu.jpg Homework Equations Above The Attempt at a Solution My attempt so far: B=C \Rightarrow \dot{\omega _1}=0 \Rightarrow \omega _1\;\text{is\;constant} \dot{\omega _2}=\omega _3 \omega _1 -...
  24. C

    Alegbra of simple harmonic motion

    Homework Statement I am wanting to learn how to rearrange equations for simple harmonic motion equations (I am new to LaTeX so gimme a break!) mostly to find time (t) as the subject, but I am not very good at rearranging equations with sin/cos etc and want to get better at it, partly homework...
  25. O

    Simple harmonic motion and static equilibrium

    Homework Statement In static equilibrium a spring is stretched 0.25 m by a hanging mass. If the system is initially moved up to the unstretched position and released with zero velocity, determine position of the mass (in m) after 4.2s. Take the equilibrium position to be zero and up the...
  26. M

    Phase Angle for Simple Harmonic Motion

    Phase Angle / Phase Question - Simple Harmonic Motion Homework Statement If I were given a function of displacement for simple harmonic motion in the form of: x = Acos(\omegat + \phi) Would the phase angle, \phi, always be the same? Say if I derived the equations into forms for...
  27. S

    Does Point A Oscillate in Simple Harmonic Motion with a Wave?

    you have a transverse sinusoidal wave on a string, and say there's a point A on that string. does point A oscillate in simple harmonic motion with a frequency that's equal to the frequency of the wave?
  28. B

    Finding the phase constant for simple harmonic motion

    Homework Statement I need to find the speed, at time t=0.015s, of a hydraulic valve component undergoing sinusoidal vibrations. The frequency of the vibrations is 25Hz, the amplitude is 2cm and the angular frequency is 157 s-1 Homework Equations The equation for speed of sinusoidal...
  29. T

    Simple Harmonic Motion Lab: Mass and Period Relationship Analysis

    Homework Statement Hi I just did a physics lab that involved a Simple Harmonic Motion. What I did was have a mass hung on a spring and then put different masses and find their Period (T) and time for 5 cycles going up and down. RESULTS: Mass (kg) 0.100 0.150 0.200 0.250 0.300...
  30. M

    Simple Harmonic Motion of a rolling ball

    Homework Statement A ball rolls on a circular track of radius 0.61 m with a constant angular speed of 1.3 rad/s in the counterclockwise direction. A. If the angular position of the ball at t= 0 is \theta= 0, find the x component of the ball's position at the time 2.6 s. Let \theta= 0...
  31. M

    Simple harmonic motion of a spring?

    Homework Statement I had a lab today and one of my questions is: "If you displace the end of the spring a little or a lot, in other words if you change the amplitude of the oscillation, the period will be the exact same. 1) How can this happen? 2) What is different about the motion of the...
  32. B

    Simple harmonic motion - vibration frequency

    I need to calculate the frequency of sinusoidal vibrations in simple harmonic motion. The only known values that I have are the acceleration amplitude and the vibration amplitude. Is there a way of calculating the frequency of vibration without knowing the period of the oscillations?
  33. C

    What is the Required Frequency for Simple Harmonic Motion Testing?

    Homework Statement I am confoosed, I think I need to find T first but not sure I am using the right equations, is vibrational amplitude both length & A? A hydraulic valve is subjected to sinusoidal vibrations to test the component under conditions of simple harmonic motion. The first test...
  34. Telemachus

    Simple harmonic motion [ I have an exam tomorrow morning]

    Simple harmonic motion [URGENT I have an exam tomorrow morning] Homework Statement Hi there. I don't know how to solve this problem about simple harmonic motion. It says: A particle of 100 grams is animated with a simple harmonic motion, which starts 20cm from its equilibrium position, where...
  35. T

    Calculating Time for Simple Harmonic Motion: Rod with Freely Rotating Object

    Homework Statement Given a rod with length it is hinged thus it can freely rotate. An object is attached to the end of the rod and it is brought all the way vertically up. Then a slight disturbance and it flies down (from equilibrium). How long does it take for it to come down to the minimum...
  36. F

    Finding the variable S using the intercept in simple harmonic motion of spring.

    In an experiment to determine g using simple harmonic motion using a harmonic oscillator, a motion sensor and data logging equipment. I have all the variables but I can't figure out how to get S in the following equation: T^2 = ((4pi^2)/k)M + ((4pi^2)/k)S ...(1) I have a graph of T^2 (the...
  37. F

    Simple Harmonic Motion Question

    Homework Statement Homework Equations x = A cos(wt-phi) The Attempt at a Solution Using the above equation for t, calculating values for t1 at -0.05 and t2 at 0.05, as well as assuming phase angle phi is zero, I get an answer of over 40 seconds. I think I may be using the wrong equation or...
  38. G

    Coulomb's Law and Simple Harmonic Motion

    Homework Statement Two positive charges +Q are affixed rigidly to the x-axis one at x = -d and the other at x = +d. A third charge +q of mass mwhich is constrained to move only in the x-axis is displaced from th eorigin by a small distance s << d and then released from rest. Show that q+...
  39. V

    Finding Velocity and Acceleration in Simple Harmonic Motion

    Please help me, Question The equation of motion of a mass is given as x = (0.2m) sin (3t). Find the velocity and acceleration of the mass when the object is +5cm from its equilibrium position.
  40. T

    Simple Harmonic Motion Homework: Finding Amplitude, Period, and Time of Travel

    Homework Statement A machaine part moves in a straight line with SHM. At positons 15mm and 20mm from the center of oscillation it has velocitys 2 m/s and 1 m/s respectively. find the amplitude and period of the motion. and the shortest time taken for the part to travel between these 2...
  41. C

    Show an electron is executing simple harmonic motion

    Homework Statement When the electron in a hydrogen atom bound to the nucleus moves a small distance from its equilibrium position, a restoring force at a given radius is given by: k = e^2/4*pi*epsilon*r^2 where r = 0.05 nm may be taken as the radius of the atom (the equilibrium radius of...
  42. H

    Simple Harmonic Motion of a Particle

    Homework Statement A particle is oscillating in simple harmonic motion with period 4.5 ms and amplitude 3.0 cm. At time t = 0, the particle is at the equilibrium position. Calculate, for this particle: a) frequency b) the angular frequency c) the maximum speed d) the maximum acceleration e)...
  43. J

    Simple Harmonic Motion, object floating in a liquid

    (apologies for the formatting, mixing LaTeX and regular text looks ugly, but I don't know how to do it otherwise) Homework Statement This is problem 3-7 from Thornton and Marion's Classical Dynamics. A body of uniform cross-sectional area A = 1 cm2 and of mass density \rho=0.8 g/cm3 floats...
  44. J

    Maximum Amplitude for Simple Harmonic Motion with Friction

    Homework Statement A disk of mass M, attached to a spring of constant k fixed to a vertical wall can oscillate freely in a frictionless horizontal plane. A small block of mass m is put on the disk with which there is friction under a coefficient of friction \mu. What is the maximum amplitude...
  45. G

    Mechanics problem about simple harmonic motion

    Hi, Can anyone help me with this question? The potential energy of mass (m=6KG) that is connected to a spring is given by: U(x) = 5x ^ 2 -10x +12 Find the period of the small fluctuations around the equilibrium point (in seconds).
  46. M

    Graph of simple harmonic motion

    Homework Statement A particle moves with amplitude A and period T (see figure). Express the following in terms of A and T and numberical constants. a) The time at which the phase is pi/2 b) maximum v c) max a d) time at which acceleration is a maximum Homework Equations The...
  47. M

    Kinematics: simple harmonic motion

    Homework Statement The motion of a particle is given by x=(6.0m) cos(0.586t +0.72) a) find amplitude b) find period c) find the first time for t>0 when v=0 d) find the max acceleration e) find the phase at time t = 1.38s Homework Equations T = 2pie/omega v = -A omega sin omega*t...
  48. M

    Simple Harmonic Motion of a pendulum

    Homework Statement Hello, I'm doing a simple pendulum lab where I measure the difference in period as I increase the length of the pendulum. Simple enough. However, I'm having trouble analyzing my graphs of a linear versus a curve fit. Can someone explain why the curved/nonlinear fit is...
  49. S

    Simple Harmonic Motion with Springs that have Mass

    Hi all, I recently learned about simple harmonic motion. In all the questions I have done, the springs are massless. I would like to know what happens when the spring has mass. I think that if the spring has mass, then the force in the spring will also have to counteract the weight of the...
  50. C

    Simple Harmonic Motion Question

    Homework Statement A particle undergoes simple harmonic with amplitude of 10cm and frequency 5Hz. If it passes through the equilibrium position (x=0) at time t = 0, calculate the position, velocity and acceleration of the particle at t = 3.5m5 ms. The Attempt at a Solution Given...
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