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.

View More On Wikipedia.org
Recent contents Top users
  1. J

    Simple harmonic motion of some mass

    Homework Statement A 0.25-kg mass is attached to the end of a spring that is attached horizontally to a wall. When the mass is displaced 8.5 cm and then released, it undergoes SHM. The force constant of the spring is 1.4 3 102 N/m. The amplitude remains constant. (a) How far does the mass...
  2. W

    Simple harmonic motion of a pendulum

    Homework Statement I need to find the phase difference between two pendulums. My problem is that I don;t seem to have enough information to calculate the phase for the second pendulum (I have already calculated the phase for the first). The pendulum is 0.35m long, and is at 0.00rad at...
  3. Z

    Simple Harmonic Motion

    There is a horizontal spring-mass system lie on top of a frictionless table. let m=mass k=spring constant x=displacement from equilibrium position A=amplitude T=period By using conventional way, time taken to complete a quarter of cycle=T/4=(∏/2)√(m/k) consider another way of doing...
  4. S

    Instances of simple harmonic motion?

    Hi, I have this simple harmonic motion lab, it can't be a simple pendulum lab where you manipulate mass or length of string, it can't be a spring with hanging weight either, I really have no idea what to do, is there any other way to demonstrate simple harmonic motion? thanks.
  5. R

    Simple Harmonic Motion and vibration

    Homework Statement A mass of 0.3kg is suspended from a spring of stiffness 200Nm-1. If the mass is displaced by 10mm from its equilibrium position and released, for resulting vibration, calculate: a) the maximum velocity of the mass during the vibration Homework Equations Angular...
  6. H

    Simple Harmonic Motion of spring

    Homework Statement Mass is attached to a spring and set into a vibratory motion. m=0.10 kg f=2.5 Hz Homework Equations f=1/2pie{sqrt(k/m)} The Attempt at a Solution Trying to find k (force constant) I tried using the equation above but I can't get the right answer...
  7. J

    Conceptual question on Simple Harmonic Motion.

    Homework Statement Given that a spring with a ball of mass m attached to it is oscillating in between x=A and x=-A where x=0 is the equilibrium position. Will the equilibrium position change when the the mass of the ball is doubled? 2. The attempt at a solution I think that the...
  8. R

    Simple Harmonic Motion vibration Question

    Homework Statement A mass of 0.3kg is suspended from a spring of stiffness 200Nm-1. If the mass is displaced by 10mm from its equilibrium position and released, for resulting vibration, calculate: a) the frequency of vibration b) the maximum velocity of the mass during the vibration c) the...
  9. QuarkCharmer

    Simple Harmonic Motion of a bolt of mass

    Homework Statement A bolt of mass 2.10×10^-2 kg moves with SHM that has an amplitude of 0.245 m and a period of 1.495 s. The displacement of the bolt is + 0.245 m when t=0. A.) Find the displacement of the bolt at time t=0.500s Homework Equations The Attempt at a Solution Part...
  10. P

    Calculating ∅ in Simple Harmonic Motion Equation x = xo + Asin(ωt + ∅)

    x = xo + Asin(ωt + ∅) I know all of the values, except for ∅. But i don't know how to get the value for ∅ The attempt at a solution: 0.349 = 0.367 + 0.413Sin(8.5 * 0.8938 + ∅) -0.018 = 0.413Sin(7.5973 + ∅) -0.04358 = Sin(7.5973 + ∅) From here on, i am confused, I tried using the...
  11. J

    Simple Harmonic motion of buoyant force

    Homework Statement a cylinder is in a deep pool of liquid. it has mass 2kg, diameter 10cm, height 15cm. the density of the liquid is 1.5g/cm^3. The cylinder is submerged up to 12cm, and let go. Show that the resulting motion is simple harmonic. Homework Equations x=Acos(wt)...
  12. K

    Simple harmonic motion of a spring mass

    Homework Statement A spring of negligible mass have an original length of 1m. A load of 2kg is later added to it, resulting in an extension of 0.1m. Then it is pulled 0.02m and released. What is the amplitude of the simple harmonic motion. erm basically I just want to know which is the...
  13. H

    How to approach a simple harmonic motion problem

    This is the question: A massless spring with a spring constant of 0.50 N/m, has a mass of 0.7 kg on its end. The maximum speed of the end is 2.5 m/s. What is the angular frequency of the system? I don't know how to approach this problem at all. I just know that omega/2pi is the...
  14. L

    Understanding the Effect of Perpendicular Components in Simple Harmonic Motion

    Homework Statement Kindly go through the attachment. (i) vcosθ in a direction parallel to OY. (ii) vsinθ in the direction perpendicular to OY. The component vsinθ has no effect along YOY' since it is perpendicular to OY My doubt is "Why the perpendicularity of vsinθ to OY...
  15. F

    Simple Harmonic Motion ) Vertical Spring

    Homework Statement A spring with spring constant 150 N/m hangs from a ceiling. A 2.00 kg mass is attached to the end of the spring and released. a) How far below its unstretched position will the mass be in equilibrium? b) How far below its unstretched position will the mass fall? c) Taking...
  16. J

    Simple Harmonic Motion Phase angle

    Homework Statement What is the initial phase angle of this graph that describes a simple harmonic motion? Homework Equations The Attempt at a Solution I don't have any clue about how to find it by watching the graph, I know only an equation to find it. Any help please.
  17. J

    Finding Period and Angular Frequency in Simple Harmonic Motion

    Homework Statement a particle moves to the right along the x-axis with a simple harmonic motion from x0 = 3.0cm in t=0 . if its position x is given by x = 4.0 cos (pi t + phi) , in cms ; find its period T. Homework Equations The Attempt at a Solution The problem ask me more...
  18. P

    Simple Harmonic Motion - Acceleration and Time Period

    Hi, I am a bit confused regarding the relation between the acceleration and time period in simple harmonic motion. This questions asks what would be one change to the motion of a car's wing mirror in case the glass was switched for a heavier one. I don't understand for example, how would...
  19. P

    Simple Harmonic Motion mass homework

    Hi, I am not very good with questions that ask me to asses a scenario qualitatively in SHM... So, if you guys can maybe guide/advise me how to go about these here: 1.A body is suspended vertically at the end of a spring that is attached to the ceiling of an elevator. The elevator moves...
  20. P

    Simple Harmonic Motion - Acceleration and Velocity

    Hi, 9 (a) Write down an equation for the displacement of a particle undergoing SHM with an amplitude equal to 8.0 cm and a frequency of 14 Hz, assuming that at t = 0 displacement is = to 8.0 cm and the particle is at rest. What I got (and this agrees with the book) was: x = 8.0 cos...
  21. S

    Rolling a half full water bottle and simple harmonic motion

    hi I am just saw this phenomenon and see if there is any links to the topic that I am learning in school. So when i rolled a half full (depends on how optimistic you are :smile:) water bottle with a certain amount of force, the bottle went back and forth for a little while before stopping...
  22. M

    Simple Harmonic Motion: Acceleration Max/Min

    Hi, i need some help for a physics question: when is acceleration at maximum and when is acceleration at minimum in a simple harmonic motion. i know when the speed is at maximum: at the equilibrium position; however, i do not know about the acceleration. Please note that direction does not matter
  23. P

    Simple Harmonic Motion - Acceleration

    Hi, :smile: Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of oscillation, f, is given by the expression: f = 1 / 2π * √(k/m) where k is the force per unit displacement between a hydrogen atom and the carbon atom and the m is the mass of a proton. (i)...
  24. A

    Simple Harmonic Motion and frequency

    Homework Statement A mass sits on a platform undergoing simple harmonic motion in the vertical direction. The mass loses contact with the platform when the amplitude exceeds 6.2 cm. What is the frequency, f (in Hz), of the platform’s vibration? Take g = 9.8ms−2. Homework Equations...
  25. A

    Simple harmonic motion and particle speed

    Motion of particle shows a max acc. of 30 m/s2 and a frequency of 120 cycles per minuet. assuming SHM determine, the amplitude and max velocity. i found the sqrt of k/m to be 12.57 even though neither was given and the frequency to 2 cycles/sec. i do not know what relations to use to work...
  26. N

    Amplitude of a simple harmonic motion equation

    if you have the equation: x(t) = Acos(ωt + ϕ) and you have the following information: A 200 g block hangs from a spring with spring constant 10 N/m. At t = 0s the block is 20 cm below the equilibrium position and moving upward with a speed of 100 cm/s. The answers give a short method of...
  27. A

    Simple harmonic motion in a string

    Homework Statement Hi I need some clarification on this question A light elastic string of natural length 50 cm and modulus 20 N has one end fastened to O on a smooth horizontal table. The other end has a particle of mass 0.4 kg attached to it and the particle is released from rest at a...
  28. K

    Simple Harmonic Motion , finding the time taken to travel an angular dispalcemnt

    1. Homework Statement Find the time taken to reach half the maximum angular displacement in a PENDULUM. Given that the bob hanging at rest was given an initial velocity of 2ms, and the length of the string is 6m. 2. Homework Equations finding the angular velocity using sqrt.(g/l)...
  29. X

    How Does Simple Harmonic Motion Influence Precision Timing Devices?

    1. Two people build precison timing devices, one with a simple pendulum, one with a simple mass-spring. Each is to have a period of 2 s. The Fg = 9.8 m/s^2. Select the appropriate parameters for this to happen. Part B - which device is more precise at the equator? 2. I have no idea :(...
  30. D

    Displacement Meter- Simple Harmonic Motion

    Homework Statement The figure attached shows the meter used to study the motion yB = bsinωt. The motion of the mass relative to the frame is recorded on the drum. If l1= 360 mm, l2= 480 mm, l3= 600 mm, m = 0.9 kg, c = 1.4 Ns/m and ω = 10 rad/s, Determine the range of the spring...
  31. S

    Simple Harmonic motion (non-calculus)

    Homework Statement Atoms in a solid are not stationary, but vibrate about their equilibrium positions. Typically, the frequency of vibration is about f = 2 E12 Hz and the amplitude is about 1.1 E-11m. For a typical atom, what is its (a) maximum speed? Homework Equations T= 1/f. v = change...
  32. J

    Evergy of Simple harmonic motion

    Homework Statement A 0.155 kg mass is attached to a spring and executes simple harmonic motion with a pe- riod of 0.63 s. The total energy of the system is 1.9 J. Find the force constant of the spring. Homework Equations E=1/2(kA^2) The Attempt at a Solution We went...
  33. D

    Simple harmonic motion spring problem

    Homework Statement The drawing shows a top view of a frictionless horizontal surface, where there are two springs with particles of mass*m1*and*m2*attached to them. Each spring has a spring constant of*120*N/m. The particles are pulled to the right and then released from the positions shown in...
  34. C

    Simple Harmonic Motion of a 2kg particle

    Homework Statement A 2kg particle undergoes simple harmonic motion according to x=1.5sin((pi*t/4) + Pi/6) A)What is the total mechanical energy of the particle? B) Shortest time for particle to go from x=.5m to x=-.75m Homework Equations Potential energy=.5kx^2 The Attempt at a...
  35. I

    Simple Harmonic Motion and Static Friction. I am stumped.

    Homework Statement During an earthquake, a floor oscillates horizontally in approximately simple harmonic motion. Assume it oscillates at a single frequency with a period of 0.84 s. After the earthquake, you are in charge of examining the video of the floor motion and discover that a box on...
  36. F

    Simple Harmonic Motion (Bullet fired into a block attached to spring)

    Homework Statement A 5g bullet is fired horizontally into a 0.50kg block of wood resting on a frictionless table. The block, which is attached to a horizontal spring, retains the bullet and moves forward, compressing the spring. The block-bullet system goes into SHM with a frequency of 9Hz...
  37. K

    Calculating SHM Parameters: Speed and Acceleration at Different Points

    A 2kg body, moving under the influence of a force constant of 3.16N/m, vibrates in SHM with an amplitude of 30mm. Determine the speed and the acceleration, a) at the midpoint of the vibration (ie. zero displacement) b) at the end of the path (ie. Max displacement) c) at a point 20mm from the...
  38. M

    Simple Harmonic Motion - Vertical Spring

    Homework Statement A block with mass m =7 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.7 m/s. The block oscillates on the spring without...
  39. M

    Simple Harmonic Motion - Velocity EQ.

    Homework Statement x = 0.20m*sin(0.44 rad/s * t) Write the equation for the velocity of this object. Find the velocity at t = 4:0 s. Homework Equations The Attempt at a Solution well, i know that v(t)= - wAsin(wt +\phi) and we know the w = 0.44 rad/s A = 0.20 s t=4...
  40. Z

    Solve the Mistake: Simple Harmonic Motion

    Homework Statement A particle executes simple harmonic motion along a straight line with mean position at x=0, period 20s and amplitude 5cm. The (shortest) time in seconds taken by the particle to got from x=4cm to x=-3cm is? The Attempt at a Solution Let the equation be x=Asin(wt+Φ)...
  41. P

    How Does SHM Affect Apparent Weight on a Fish Scale in Water Waves?

    Homework Statement A man floating in water was spotted by fishermen on a boat. Before taking him on board, the man was put on a fish scale to see how much he weighed. The reading on the scale oscillated between 72kg and 178kg. The wave speed was measured to be 16 m/s. The wave height was 3 m...
  42. P

    Spring mass system and Simple harmonic motion

    Homework Statement A block of mass 300 gm is attached to a spring with spring constant 1000 N/m. A smaller block of mass 100 gm is pushed against the first block, compressing the spring 5 cm. The coefficient of static friction between the two blocks is u = 0.2. The blocks are then released...
  43. P

    How Does Simple Harmonic Motion Depend on Pendulum Length and Gravity?

    Homework Statement 1. Modeling. Functions. A student measures the length L = 3 feet of a light (0.1 grams) string and the mass m = 7 kilograms of a small (radius of 0.0005 inches) bob at the end of the string. The students also knows the value of acceleration due to gravity g = 9.8...
  44. I

    Exploring Simple Harmonic Motion Equations: Damping vs. Driving Force

    (This isn't homework) I've been crating some notes, and noticed that we haven't been told one equation. I know for: \frac{d^2 x}{dt^2} = \frac{-kx}{m} -\frac{b}{m} \frac{dx}{dt} I know the displacement is: x = A \omega e^{-bt/2m} cos(\omega t+ \phi) [Ie damping] I know for...
  45. B

    Simple Harmonic Motion- Phase Shift Help

    Homework Statement A 590.0 g mass oscillates with an amplitude of 11.4 cm on a spring whose spring constant is 27.7 N/m. At t=0.00 s the mass is 3.14 cm to the right of the equilibrium position and moving to the right. Homework Equations x(t)=Acos(Wt + phi) The Attempt at a Solution...
  46. Z

    Simple Harmonic Motion - Finding period of oscillation of block

    Homework Statement In the given figure, all the springs and pulley are ideal and surface is frictionless. The rod is massless. The time period of horizontal oscillations of the block is? The Attempt at a Solution I used two different approaches and both give different and wrong...
  47. S

    Calculating period of oscillation of simple harmonic motion

    Homework Statement A body is undergoing S.H.M. of amplitude 4 x 10-2 m and with a maximum speedo f 0.20m s-1. Calculate the period of the oscillation given that the velocity, v, of a body undergoing S.H.M. is ""v= omega sq.rt of A^2 - x ^2"" , where trl is the angular velocity, A is the...
  48. D

    Simple harmonic motion mass attached to spring with charge and in an E field

    A block having mass m and charge +Q is connected to a spring having constant k. The block lies on a frictionless horizontal track, and the system is immersed in a uniform electric field of magnitude E, directed as shown in the figure below. The block is released from rest when the spring is...
  49. G

    Simple Harmonic Motion: Block dropped onto a spring

    Homework Statement A 2-kg block is dropped from a height of 0.45 m above an uncompressed spring. The spring has an elastic constant of 200 N/m and negligible mass. The block strikes the end of the spring and sticks to it. (a) Determine the speed of the block at impact (b) Determine the period...
  50. A

    Simple harmonic motion of two pendulums

    Homework Statement Two pendulums of time periods 3s and 7 s respectively start oscillating simultaneously from two opposite extreme positions. After how much time they will be in the same phase? Homework Equations The Attempt at a Solution Now what exactly is the question...
Back
Top