Harmonic motion Definition and 1000 Threads

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

    SPRING CONSTANT- simple harmonic motion

    I'm investigating damped oscillations using a mass held between two springs. In the experiment, I measured the spring constant using a method which now doesn't make sense. I measured it by hanging masses from ONE vertical spring and graphing the force exerted by spring (mass times 9.8)...
  2. H

    Simple harmonic motion problem.

    x=xocos(2pi t/T), where xo is the maximum amplitude of oscillation and T is the period of oscillation. Find expressions for the velocity and acceleration of a car undergoing simple harmonic motion by differentiating x. [Answer: a=–(2pi/T)^2(Xo)cos(2pi t/T).] QUESTION: If xo = 0.3 m and T...
  3. D

    Simple harmonic motion of a car

    A 1000 kg car carrying two 100 kg football players travels over a bumpy "washboard" road with the bumps spaced 3.0 m apart. The driver finds that the car bounces with a max amplitude when he drives at a speed of 5.0 m/s. The car then stops and picks up three more 100 kg passengers. By how much...
  4. D

    Simple Harmonic Motion & a vertical spring

    Homework Statement A spring is standing upright on a table with its bottom end fastened to the table. A block is dropped from a height of 3.0 cm above the spring. The block sticks to the top end of the spring and then oscillates with an amplitude of 10 cm. What is the oscillation frequency...
  5. S

    Simple harmonic motion of coil spring

    hi i ned a little help with this problem please. An object is connectedto a 100 coil spring, that is hanging from the ceiling. The spring stretches by 0,160m. What is the spring constant? Im not sure how to go about with this...is the force 100? please help. Thanks
  6. T

    Springs - simple harmonic motion

    my question is: is there a way to find the work done to a spring when the only variable given is the distance (x)?? Homework Statement For the pressure gauge, what work is done by the air on the spring? Homework Equations W = 1/2kx2 Fx = kx The Attempt at a Solution I can't...
  7. W

    Simple harmonic motion and oscillation

    A 780-g mass is attached to a vertical spring and lowered slowly until the mass rests at its equilibrium position 30 cm below the original length of the spring. It is then set into simple harmonic motion. (a) What is the frequency and period of the oscillation? (b) What is the maximum...
  8. Ed Aboud

    Simple Harmonic Motion Equation with Period and Initial Conditions

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  9. C

    Average value of a function and simple harmonic motion

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  10. R

    Simple Harmonic Motion Maxiumum Velocity

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  11. S

    Simple harmonic motion, spring, block on block, static friction help

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  12. S

    Simple harmonic motion, finding displacement given time

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  13. C

    Solving a Harmonic Motion Problem: Finding Position, Velocity, and Acceleration

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  14. R

    Homework question concerning simple harmonic motion

    Homework Statement A system has a period of 3 seconds. The 4 kg mass oscillates with an amplitude of 0.7 meters. At what position is 50% of its energy in the form of kinetic energy and what is its velocity then? Homework Equations work = Potential energy + Kinetic energy (1/2)kA^2 =...
  15. P

    What Is the Spring Constant and Angular Frequency of a Block-Spring System?

    Homework Statement A spring is hung from the ceiling. A 0.400 kg block is then attached to the free end of the spring. When released from rest, the block drops 0.150 m before momentarily coming to rest. (a) What is the spring constant of the spring? (b) Find the angular frequency of...
  16. P

    Simple Harmonic Motion: Calculating Speeds of Blocks with a Compressed Spring

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  17. R

    Harmonic Motion of Pendulum on Mars

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  18. I

    Simple Harmonic Motion, Finding Time

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  19. S

    Solving Simple Harmonic Motion Problems

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  20. A

    Can someone check my logic? simple harmonic motion.

    Homework Statement Is the daily movement of a student from home to school and back simple harmonic motion? Homework Equations The Attempt at a Solution I don't think it is. This type of movement is linear. It involves distance, speed and so on. It does not follow a sinusoidal...
  21. S

    Simple Harmonic Motion (Mass on a Spring)

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  22. S

    Dampened Harmonic Motion and oscillation

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  23. B

    Simple Harmonic Motion of a Pendulum

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  24. B

    Simple Harmonic Motion question

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  25. K

    Energy in simple harmonic motion

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  26. U

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  27. K

    Elastic Collisions and Harmonic Motion

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  28. I

    Simple Harmonic Motion of a wave

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  29. X

    Simple harmonic motion and friction

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  30. P

    Please help with this simple harmonic motion question.

    Homework Statement A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion the block oscilates back and forth with an angular frequency of 7.0 rad/sec. The drawing indicated the position of the block when the spring is unstrained...
  31. P

    Simple Harmonic Motion of a gun

    (1)It takes a force of 75 N to compress the spring of a toy popgun 0.18 m to "load" a 0.14 kg ball. With what speed will the ball leave the gun? I used the equation F=kx I solved for K and I got 416 N/m Then I used the equation omega = square root(K/M) I solved for omega and i got 54.5...
  32. P

    Elasticity and simple harmonic motion

    A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed 0.12 m, it experiences a maximum acceleration of 19...
  33. C

    Displacement in Simple Harmonic Motion

    1. Hi! I am new to this forum. I was wondering if someone could help me with this problem. Thanks in advance! A 0.27 kg mass is suspended on a spring that stretches a distance of 4.9 cm. The mass is then pulled down an additional distance of 12.5 cm and released. What's the displacement from...
  34. M

    Simple Harmonic Motion Equation Question

    HELP-SEE LAST POST-I HAVE NO IDEA WHY THIS IS WRONG (SEE LAST POST) Homework Statement A spring with spring constant 230 N/m vibrates with an amplitude of 12.0 cm when 0.380 kg hangs from it. (a) What is the equation describing this motion as a function of time? Assume the mass passes...
  35. M

    Simple Harmonic Motion - Potential and Kinetic Energy?

    Homework Statement A 2.00 kg mass vibrates according to the equation x = 0.470 cos 8.36t, where x is in meters, and t is in seconds. Assume that x = 0.29 m. (a) Determine the amplitude. .470 (b) Determine the frequency. 1.331 (c) Determine the total...
  36. M

    How Is Spring Constant Calculated in Simple Harmonic Motion?

    Homework Statement A fisherman's scale stretches 3.4 cm when a 3.3 kg fish hangs from it. (a) What is the spring constant? (b) What will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down?Homework Equations...
  37. M

    Quick Question - Simple Harmonic Motion - (I think I just need a formula)

    Homework Statement If a particle undergoes Simple Harmonic Motion with amplitude 0.34 m, what is the total distance it travels in one period? Homework Equations x=Asin(wt+theta) The Attempt at a Solution I know A, (.34), yet it seems like this problem doesn't give me nearly...
  38. M

    Simple Harmonic Motion: Determine Velocity at t=0.250s

    _{}b]1. Homework Statement [/b) The position of a 39.8 g oscillating mass is given by the equation x(t)= (2.00cm)cos(5t- 4.00\pi) where t is in seconds. Determine Velocity at t= 0.250s M= 39.8 g T= 1.2575 rad/s K= 9.95e-1 N/m initial postion= 2 cm Homework Equations V_{x}=...
  39. ~christina~

    Helium balloon and simple harmonic motion

    Homework Statement A light baloon filled wiht helium and with a density of 0.180kg/m^3 is tied to a light string of length L= 3.00m. The string is tied to the ground, forming an "inverted" simple pendulum. The balloon is displaced slightly from it's equillibrium position, as shown in picture...
  40. ~christina~

    Block- spring- bullet- harmonic motion

    [SOLVED] Block- spring- bullet- harmonic motion... Homework Statement Your assignment is to make measurements of the muzzle velocity of a bullet. This measurig device consists of a 10kg block which rests on a horizontal surface of negligible mass and is attatched to a hooke's law spring...
  41. K

    Simple Harmonic Motion and maximum velocity

    [SOLVED] Simple Harmonic Motion I'm really having a hard time solving these two problems. 1. Objects of equal mass are oscillating up and down in simple harmonic motion on two different vertical springs. The spring constant of spring 1 is 174 N/m. The motion of the object on spring 1 has twice...
  42. A

    Deriving angular frequency for simple harmonic motion

    Homework Statement Derive the equation for angular frequency for simple harmonic motion of a spring. Homework Equations Derive omega = sqrt(k/m) from F = -kx (sorry i don't know how to use notation) The Attempt at a Solution I asked my teacher how to do this, and he used some...
  43. V

    How Do You Calculate the Damping Constant in Damped Harmonic Motion?

    Homework Statement Hi all, A hard boiled egg, with a mass m=51g, moves on the end of a spring, with force constant k=26N/m. It's initial displacement is 0.300m. A damping force F^{}x=-bv^{}x acts on the egg and the amplitude of the motion decreases to 0.106m in a time of 5.45s. Calculate the...
  44. R

    Exploring Damped Harmonic Motion

    Concerning damped harmonic motion (eg. mass on a spring, using cardboard discs as dampers); for the equation (below) of the graph describing the effect of different sized dampers on the time taken for amplitude of oscillations to halve, what would b (y-intercept) and n (gradient) represent...
  45. S

    Differential equations - harmonic motion

    Homework Statement A mass of 5 kilograms dangles from a spring, stretching the spring centimeters when in equilibrium. The mass oscillates vertically in a fluid, with a frictional force times its speed. If initially it starts from rest at an extension below the equilibrium point of...
  46. R

    Exploring b & n in Damped Harmonic Motion

    Homework Statement Concerning damped harmonic motion (mass on a spring using cardboard discs as dampers); for the equation (below) of the graph describing the effect of different sized dampers on the time taken for amplitude of oscillations to halve, what do b (y-intercept) and n (gradient)...
  47. S

    Harmonic Motion with Multiple Springs - Examples & Discussion

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  48. M

    Simple Harmonic Motion position and velocity problem

    "A particle moves along the x-axis. It is initially at the position 0.270 m, moving with velocity 0.140 m/s and acceleration -0.320 m/s^2. Assume it moves with simple harmonic motion for 4.50 s and x=0 is its equilibrium position. Find its position and velocity at the end of this time...
  49. D

    Simple Harmonic Motion & Pendulum Problems Need HELP

    Question 1: A 0.1 kg block attached to a spring of force constant 16.9 N/m oscillates with an amplitude of 6 cm. Find the maximum speed of the block. Answer in units of m/s. Question 2: Find the speed of the block when it is 3 cm from the equilibrium position. Answer in units of m/s. Question...
  50. ~christina~

    Simple harmonic motion of a particle

    Homework Statement A particle moves along x-axis It is initially at 0.270m moving with velocity of 0.140m/s and acceleration of -0.320m/s^2 Suppose it moves with constant acceleration for 4.50s. Find it's: a) position and velocity at end of time interval next assume it moves with...
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