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. L

    Quick question about a simple harmonic motion problem

    Homework Statement The position of a particle is given by x = 4.6 cos (pi)t, where x is in meters and t is in seconds. (a) Find the maximum speed and maximum acceleration of the particle. I've already solved these by finding the first and second derivatives of the above x. v =...
  2. L

    Simple Harmonic Motion formula help

    Homework Statement A small bock that has a mass equal to M rest on a piston that is vibrating vertically with simply harmonic motion described by the formula y = Asin(wt) a) Show that the block will leave the piston if w2A > g. b) If w2A = 3g and A = 15 cm, at what time will the block...
  3. Z

    Solving SHM: Find Amplitude, Velocity & Time

    A body with SHM has a velocity of 1.3 m/s at a distance of 1.0m from the mean position, and a velocity of 1.0 m/s at a distance of 1.3m from the mean position. Find: a) The amplitude of the motion. b) The velocity of the mid-position. c) The time elapsed between the instants when the body...
  4. E

    Simple Harmonic Motion troubles.

    Homework Statement Two 100g blocks are held 80 cm above a table. As shown in the figure, one of them is just touching a 80cm-long spring. The two blocks are released at the same time. The block on the left just hits the table at exactly the same instant as the block on the right first...
  5. B

    Simple Harmonic Motion: 1 Cycle = 1 Oscillation?

    Is 1 cycle the same as 1 oscillation?
  6. L

    Time of maximum displacement in simple harmonic motion?

    I am completely and totally lost... Homework Statement The motion of an object is simple harmonic with equation of motion x = (27.1 m) sin(16.0 t /s + 0.7). At what time after t = 0 will the displacement reach its first maximum (where velocity equals zero)? Homework Equations x = Asin(wt)
  7. J

    Simple Harmonic Motion an Object Attached to a Spring

    Simple Harmonic Motion .. an Object Attached to a Spring! Hi everybody :smile: .. I'm glad that i joined this forum so that i can help people and benefit at the same time :) .. i wanted to start with this problem right here ,, and hope that i get the hand from you :) it's a question I've...
  8. C

    Simple Harmonic Motion (will be the death of me)

    Homework Statement The motion of an object is simple harmonic with equation of motion x = (27.1 m) sin(16.0 t /s + 0.7). At what time after t = 0 will the displacement reach its first maximum (where velocity equals zero)? Homework Equations (displacement)=Asin(freq.*t+phase) The...
  9. L

    Proving Simple Harmonic Motion: Amplitude and Frequency Analysis

    Homework Statement Prove that there exists a number A>0 and \phi such that acos(ct)+bsin(ct)=Acos(ct-\phi). Homework Equations a,b,c are predermined constants where c>0. From this equation I can justify conclusions regarding the amplitude, frequency, and so forth of a simple harmonic...
  10. T

    Simple Harmonic Motion: Spring Motion

    A 2.1 g spider is dangling at the end of a silk thread. You can make the spider bounce up and down on the thread by tapping lightly on his feet with a pencil. You soon discover that you can give the spider the largest amplitude on his little bungee cord if you tap at a frequency of 0.8 Hz. What...
  11. T

    Simple Harmonic Motion: Pendulum

    The Earth's acceleration due the gravity varies from 9.78 m/s2 at the equator to 9.83 m/s2 at the poles. A pendulum whose length is precisely 1.000 m can be used to measure g. Such a device is called a gravimeter. (a) How long do 100 oscillations take at the equator? (in sec) (b) How long...
  12. T

    Simple Harmonic Motion: Oscillator

    An oscillator with a mass of 600 g and a period of 0.50 s has an amplitude that decreased by 2.0% during each complete oscillation. If the initial amplitude is 6 cm, what will be the amplitude after 25 oscillations? I should most likely be using T = 2pi*sqrt L/g, as well as the many...
  13. T

    Springs: Simple Harmonic Motion

    A compact car has a mass of 1050 kg. Assume that the car has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs. (a) What is the spring constant of each spring if the empty car bounces up and down 2.0 times each second...
  14. H

    Simple Harmonic Motion, velocity and acceleration

    Homework Statement a body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x=5.0 sin (pi*(t) + pi/3). What is the velocity in m/s and acceleration in m/s^2 of the body at t=1.0s? Homework Equations x(t) = A cos...
  15. C

    Simple Harmonic Motion: Maximum Speed of a Grandfather Clock Pendulum in cm/s

    Homework Statement A grandfather clock is constructed so that it has a simple pendulum that swings from one side to the other, a distance of 22.0 mm, in 1.00 s. What is the maximum speed of the pendulum bob? Use two different methods. First, assume SHM and use the relationship between...
  16. B

    Simple Harmonic Motion: Finding the Position of a Block at 0.69 seconds

    Homework Statement A block of mass 0.678 kilograms is suspended from a spring with a spring constant of 28.6 Newtons per meter. When the block is at rest, it is located 1.44 meters above the floor. The block is then set into oscillation by being lifted to a height of 1.83 meters and...
  17. L

    Box floating in a liquid and undergoing simple harmonic motion

    Homework Statement A box is floating in a liquid. It is pushed down then released to oscillate. How do I determine the period of this oscillation? No idea where to go with this one. Homework Equations The Attempt at a Solution
  18. G

    Newton's Cradle, Simple Harmonic Motion

    Is it possible to see Newton's cradle in simple harmonic motion? Im thinking that the period is the same as a simple pendulum, if not how would I calculate this?
  19. S

    Simple Harmonic Motion and a Car

    Homework Statement A car uniformly accelerates. Show an open door that slams shut will do so in simple harmonic motion.Homework Equations The Attempt at a Solution This seems more conceptual than mathematical. I considered using T = Ia but the problem is the torque would act on the pivot (point...
  20. H

    Simple Harmonic Motion and friction

    Homework Statement Mass m moves along a line on a rough table and is attached on either side to a stretched spring (both have equal spring constants k). The coefficients of static and sliding friction between mass and the table are equal with value \mu (a) show in the abscence of friciton...
  21. J

    How Do You Calculate Simple Harmonic Motion Parameters for a Spring System?

    If you couldn't tell I am new to the board so any tips would be appreciated :) edit once again, I am sorry for not showing work but i really don't understand it, when i do the work i just kinda wing it and throw stuff together Homework Statement As shown a 0.5 kg mass is attached to a spring...
  22. K

    Find amplitude with SHM (Simple Harmonic Motion)

    Homework Statement It is a three part question in which I have successfully answered the first two of the questions. Part. 1 A weight suspended from a spring is seen to bob up and down over a distance of 10 cm twice each second. What is the frequency? 2 Hz is the...
  23. M

    Simple Harmonic Motion - what is its new period

    A uniform meter stick is hung at its center from a thin wire. It is twisted and oscillates with a period of 5 s. The meter stick is then sawed off to a length of 0.76 m, rebalanced at its center, and set into oscillation. what is its new period I= 1/12 mL^2 equation: T= 2 pi * sqrt (I/k) where...
  24. V

    Thermodynamics and simple harmonic motion

    Homework Statement A horizontal piston-cylinder system containing n mole of ideal gas is surrounded by air at temperature T_{0} and pressure P_{0}. If the piston is displaced slightly from equilibrium, show that it executes simple harmonic motion with angular frequency...
  25. jacksonpeeble

    Energy and simple harmonic motion

    Homework Statement A 74.4-kg bungee jumper is standing on a tall platform (h0 = 46.6 m). The bungee cord has an unstrained length of L0 = 9.54 m and, when stretched, behaves like an ideal spring with a spring constant of k = 61.8 N/m. The jumper falls from rest, and it is assumed that the only...
  26. I

    Simple Harmonic Motion and displacement

    1. A 0.69 kg block is hung from and stretches a spring that is attached to the ceiling. A second block is attached to the first one, and the amount that the spring stretches from its unstrained length increases by a factor of 5. What is the mass of the second block? 2. Force= spring...
  27. jacksonpeeble

    Conservation of Energy, Simple Harmonic Motion

    Homework Statement A 0.200-m uniform bar has a mass of 0.790 kg and is released from rest in the vertical position, as the drawing indicates. The spring is initially unstrained and has a spring constant of k = 20.0 N/m. Find the tangential speed with which end A strikes the horizontal surface...
  28. C

    Simple Harmonic Motion of a Rigid Body

    Homework Statement A very light, rigid rod with a length of 0.570 m extends straight out from one end of a meter stick. The stick is suspended from a pivot at the far end of the rod and is set into oscillation. Determine the period of oscillation. Homework Equations omega =...
  29. F

    Using Simple Harmonic motion and conservation of motion to find maximum velocity

    The Question Relevant equations KE=0.5*m*v^2 T=2*pi*sqrt(m/k) EE=0.5*k*x^2 KEi+UEi=KEf+UEf I think that's all of them attempt at a solution I was thinking about just using the conservation of energy at the the equilibrium point, as the kinetic energy would be at a max there and...
  30. T

    Simple harmonic motion frictionless block problem

    Homework Statement A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of 6.6 rad/s. The drawing indicates the position of the block when the spring is unstrained...
  31. R

    Building this graph of simple harmonic motion

    Homework Statement Hey I'm building a graph of period squared vs. mass for simple harmonic motion finding the slope and getting K for a spring. since T^2 = ((4*pi^2)/k)m the slope is (4*pi^2)/k so I get my slope from my graph and it has an uncertainty of +- 0.2 to get K we...
  32. C

    Vertical simple harmonic motion concept

    Homework Statement A 0.12-kg block is suspended from a spring. When a small stone of mass 30 g is placed on the block, the spring stretches an additional 5 cm. With the stone on the block, the spring oscillates with an amplitude of 12 cm. What is the net force of the stone when it is at a point...
  33. I

    Simple harmonic motion question

    Simple harmonic motion question! Homework Statement A mass undergoing simple harmonic motion has a displacement of X = 0.5 m and V = 4 m/s at one time and x=.25 and V = -8. what is the period of this oscillation? Homework Equations X(t) = Acos (wt + phi) V(t) = -Awsin (wt + phi)...
  34. B

    Simple harmonic motion diff. equation

    Homework Statement A mass of 1 slug is suspended from a spring whose spring constant is 9 lb/ft. The mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of \sqrt{3} ft/s. Find the times at which the mass is heading downward at a velocity of 3...
  35. M

    Simple Harmonic Motion of mass is suspended by a spring

    A mass is suspended by a spring. The mass is pulled down and released at t=0. The equation for its displacement x in m from the equilibrium position is x = 0.050 cos(πt). π = pi = 3.14159 for clarification (because it looks like an n for some reason) (a) What is (i) the amplitude, (ii) the...
  36. I

    Simple Harmonic Motion, Velocity at a certain time

    Homework Statement The velocity of an object in simple harmonic motion is given by v(t)= -(0.347 m/s)sin(15.0t + 2.00π), where t is in seconds. What is the first time after t=0.00 s at which the velocity is -0.100 m/s? Homework Equations The Attempt at a Solution -0.1 = -(0.347)sin(15t...
  37. J

    Didn't learn simple harmonic motion in physics 1, will this hurt me?

    I took calc-based physics 1 last semester, but since it was at a community college, I don't think we went as far as the 4 year universities went. We skipped over simple harmonic motion. Will this hurt me later on, when I go to mid-level and upper-level physics courses at the 4-year university...
  38. G

    Archived Pendulum Motion (Simple Harmonic Motion)

    Homework Statement A 180 g mass on a 2.5m long string is pulled 6.6 degrees to one side and released. How long does it take for the pendulum to reach 2.7 degrees on the opposite side?Homework Equations omega = sqrt(g/L) theta = S/L theta(t) = A * cos(omega * t + phi) The Attempt at a...
  39. K

    Why is Angular Frequency Important in Simple Harmonic Motion Analysis?

    1. Angular frequency is introduced into the analysis of simple harmonic motion because: 1. Because the unit of hz is not a convnient unit for frquency. 2. to create a mathematical relationship between displacement and time. 3. To create a link between mass and frequency of vibration. 4...
  40. V

    Calculating Position in Simple Harmonic Motion with Given Amplitude and Velocity

    Homework Statement A moving particle displays simple harmonic motion with an amplitude of 3 cm. What position will it be for it to have half of its maximum speed? Homework Equations vmax= omega*A The Attempt at a Solution I divided the amplitude by 2 but I believe that's an...
  41. E

    Damped simple harmonic motion question

    Homework Statement The frequency fd of a damped oscillator is 100 Hz, and the ratio of the amplitudes of two successive maxima is one half. What is the undamped frequency f0 of this oscillator?Homework Equations this is the equation in my textbook for the position at time t of an underdamped...
  42. M

    Is a simple pendulum simple harmonic motion?

    I'm wondering this because my textbook says that for small angles it is, but we learned that for simple harmonic motion to occur there must be a linear restoring force.. eg F= -kx.. but for the simple pendulum the restoring force is F= -mgsin(theta).. wouldn't this not be linear?
  43. P

    Simple harmonic motion with an amplitude

    Homework Statement A block of unknown mass is attached to a spring with a spring constant of 5.50 N/m and undergoes simple harmonic motion with an amplitude of 12.5 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 25.0 cm/s. (a)...
  44. B

    Simple Harmonic Motion: Finding Frequency and Potential Energy Function

    Homework Statement a particle of mass m moves in one dimension with an applied force Fx=-Fosinh(\alphax) where \alpha and Fo are constants. find the frequency of small oscillations about the equilibrium position. next, find the potential energy function and sketch it. Homework Equations...
  45. V

    PHYSICS: Poschel-Teller Potential and Natural Frequency Derivation

    Homework Statement A particle of mass m moves in the one dimensional Poschel-Teller potential V(x). Find an expression for the natural frequency of small oscillations. Homework Equations V(x) = -V_{0}sech^{2}(x/\lambda) The Attempt at a Solution I am making the uncertain assumption that...
  46. I

    Simple Harmonic Motion of a spring and a mass

    Homework Statement A spiral spring of natural length 300mm is suspended vertically from a fixesd point with ita upper end fixed .A mass of 0.150 kg is suspended at rest from the lower end of the spring to increase its length to 355mm.The mass is then pulled down a further distance of 30 mm...
  47. M

    Why Not Consider Piston Oscillations as Simple Harmonic Motion?

    i have asked this question before ,yet i ask again, why should we not consider the reciprocating action of the piston as simple harmonic motion? harmonic oscillations are when a particle may oscillate within unequal limits about the mean position a special case in which limits of...
  48. I

    Calculating Simple Harmonic Motion for a Mass on a Spring - Homework Example

    1. Homework Statement [/b] 1)For a mass on a spring,using k=10N/m,m=1kg and amplitude =0.1m.calculate the following: *The displacement 0.2s after release. *The Time-period of oscillation. *The max. Velocity. *The max acceleration. Homework Equations x=Acos\varpit (for...
  49. P

    Relate simple harmonic motion to circular motion

    1. Prove that the maximum speed of a mass on a spring is given by Vmax = 2pifA f = frequency A= amplitude We have just learned how to relate simple harmonic motion to circular motion. So I am dealing with some of those equations. 3. While writing this out I kind of had a thought and...
  50. T

    Simple Harmonic Motion MCQ Question

    Homework Statement A simple pendulum was moving in front of a horizontal scale. the extreme positions of the bob were at the 300mm and 500mm marks. The bob moved from the 350mm to the 450mm marks in 1.0s. What is the period of the oscillations? A. 2.0s B. 3.0s C. 4.0s D. 6.0s Homework...
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