What is Harmonic motion: Definition and 1000 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. A

    Second Order Runge Kutta for Simple Harmonic Motion

    Homework Statement The ordinary differential equation describing shm is d^2x/dt^2=-w^2x where x is the displacement, t is the time and w is the frequency. If x=0 at t=0, the analytical solution is x=Asin(wt), where A is the amplitude. 1) Rewite equation 1 as two first oder ode's suitable for...
  2. moenste

    Particle moving with simple harmonic motion

    Homework Statement A particle moves with simple harmonic motion in a straight line with amplitude 0.05 m and period 12 s. Find: (a) the maximum speed, (b) the maximum acceleration, of the particle. Write down the values of the constants P and Q in the equation x / m = P sin [Q (t / s)] which...
  3. Pao44445

    B Simple Harmonic Motion: Finding Amplitude, Velocity, and Acceleration

    I am studying about SHM but I don't know how to find an amplitude,velocity,acceralation of motio. I know the formula but I don't understand where it came from x = Asin(omega(t))
  4. J

    Simple Harmonic Motion - Getting Acceleration from Velocity

    Homework Statement I am doing an experiment where I am measuring the force a speaker is exerting when it is driven by a certain voltage and frequency, so my voltage and frequency values are known. I am assuming the speaker is undergoing SHM and I am measuring its peak to peak velocity...
  5. Vanessa Le

    Simple Harmonic Motion with Rotational Inertia

    Homework Statement One end of a light spring with force constant k = 100 N/m is attached to a vertical wall. A light string is tied to the other end of the horizontal spring. the string changes from horizontal to vertical as it passes over a pulley of mass M in the shape of a solid disk of...
  6. R

    Non-Harmonic Pendulum: Calculating Gravity g

    If the Pendulum doesn't follow Harmonic Motion can we still use the formula 1) T = 2π Root(L/g) ? 2) If not, how can I calculate gravity g?
  7. M

    MHB Simple Harmonic Motion: 5kg Particle Suspended by 500 N/m String

    A particle of mass 5 kg is suspended from a fixed point by a light elastic string which hangs vertically. The elastic constant of the string is 500 N/m. The mass is pulled down a vertical distance of 20 cm from the equilibrium position and is then released from rest. (i) Show that the particle...
  8. TheCapacitor

    Measuring young's modulus from simple harmonic motion

    Homework Statement I was doing this experiment: http://practicalphysics.org/shm-cantilever.html I'm interested in the derivation of the result ω^2 = Exy^3 / 4*M*L^3. I tried to think where it comes from. How do we even start to derive k from the equation mg = KS where S is the delta in the...
  9. X

    Harmonic Motion and uniform disk of mass

    Homework Statement A uniform disk of mass m and radius R lies in a vertical plane and is pivoted about a point a distance ℓcm from its center of mass in (Figure 1) . When given a small rotational displacement about the pivot, the disk undergoes simple harmonic motion. Determine the period of...
  10. X

    Finding Velocity in Simple Harmonic Motion

    Homework Statement The position of a particle undergoing simple harmonic motion is given by x(t)=35cos(10πt), where x is in millimeters and t is in seconds. Determine the x component of velocity of the particle at t = 0.60 s . Homework Equations v = x/t The Attempt at a Solution I correctly...
  11. M

    MHB When does the elastic string become slack in simple harmonic motion?

    A particle of mass m is suspended from a point p on the ceiling by means of a light elastic string of natural length d and elastic constant of 49m/d. it is pulled down a distance 8d/5 below p and released from rest. (i) show it will preform SHM as long as the string remains taut. (ii) find in...
  12. Erenjaeger

    Simple harmonic motion problem

    Homework Statement A 45.0-g object connected to a spring with a force constant of 40.0 N/m oscillates with an amplitude of 6.00 cm on a frictionless, horizontal surface. a) find the total energy of the system (mJ)[/B]Homework Equations 1/2KA^2 [/B]The Attempt at a Solution Is the force...
  13. Clara Chung

    Simple Harmonic Motion: Pendulum Oscillation Calculation

    Homework Statement A pendulum of length 2.0 m makes small angle oscillations with an amplitude of 15 degrees. a) Find the time required for the bob to oscillate from 5 degrees to 10 degrees to the right. b)Calculate the velocity and acceleration at these two positions. Homework Equations ω^2...
  14. P

    Harmonic Motion with External Force: Impact on Period?

    Homework Statement A particle with mass m is undergoing with harmonic motion with a period T, we introduce an external force F proportional to velocity v so that F= -bv with b a constant and we assume that the particle continues to oscillate how does the period change? Homework Equations F= m...
  15. A

    Simple harmonic motion (with calculus)

    Homework Statement An object with mass m undergoes simple harmonic motion, following 2 perpendicular directions, described by the equations: x=a cos (wt), a>0, y=b cos (2wt), b>0 a) find the equation of the trajectory b) find the speed at any given time (so having t as a variable) c) the...
  16. B

    Kinetic Energy from a Simple Harmonic motion and spring

    Homework Statement A 0.26-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 190 N/m. The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes...
  17. Nipuna Weerasekara

    A Simple Harmonic Motion Question

    Homework Statement As in the given picture, the cylinder is drowned (not completely drowned as in partially drowned) in water. The cylinder is attached with a spring which has the spring constant of 200 N/m. The spring has attached to a unmovable point in the ceiling. The weight of the...
  18. MaxBicknell

    Simple harmonic motion solved for time

    Homework Statement A particle of mass 0.50 kg performs simple harmonic motion along the x-axis with amplitude 0.55m and period 4.3 seconds. The initial displacement of the particle is -0.30 m and it is traveling in the positive x-direction. The phase constant of the motion (Φ) = -2.15 rad...
  19. ryanuser

    Simple harmonic motion problem

    Homework Statement A body performaning simple harmonic motion has a displacement x given by the equation x= 30 sin 50t, where t is the time in seconds. what is the frequency of the oscillation? Answers are: A. 0.020Hz B. 0.13Hz C. 8.0Hz D. 30Hz E. 50Hz (correct...
  20. RoboNerd

    Graphs relating to simple harmonic motion

    Homework Statement Homework Equations None. The Attempt at a Solution Hi everyone. Apparently 5 is the right answer, although I chose D. Could anyone please weigh in with their thoughts about why 5 is right and my answer is apparently wrong? Thanks!
  21. Rorshach

    Difference between two harmonic motion equations

    Homework Statement Hello, folks:) I'm currently having problem with properly understanding the difference and aplications of two equations which resemble each other greatly, but the difference makes it difficult for me to tell exactly which one is for what. 2. Homework Equations Those two...
  22. i_hate_math

    Simple Harmonic Motion and Energy Problem

    Homework Statement In the figure, block 2 of mass 2.40 kg oscillates on the end of a spring in SHM with a period of 26.00 ms. The position of the block is given by x = (1.80 cm) cos(ωt + π/2). Block 1 of mass 4.80 kg slides toward block 2 with a velocity of magnitude 6.90 m/s, directed along...
  23. i_hate_math

    Easy Simple Harmonic Motion Problem

    Homework Statement Two particles oscillate in simple harmonic motion along a common straight-line segment of length 1.5 m. Each particle has a period of 1.5 s, but they differ in phase by π/5 rad. (a) How far apart are they 0.46 s after the lagging particle leaves one end of the path? (b) Are...
  24. S

    Simple Harmonic Motion Problem

    Homework Statement A 12.0-N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as a function of time t is given by: y(t)=4.50cmcos[(19.5s−1)t−π/8]. (a) What is the spring constant of the spring? (b) What is the maximum...
  25. C

    Periodic Time Calculation for Simple Harmonic Motion with a Spring

    Homework Statement A 0.61 kg mass attached to a spring (k = 27 N m-1) is performing SHM on a smooth horizontal surface. Calculate the periodic time of these oscillations. Homework Equations ω=2π/T ω=2πƒ The Attempt at a Solution I think I need to find out the angular frequency ω of the...
  26. M

    What is the relationship between force and time in simple harmonic motion?

    For the lab I have to find the spring constant and how force relates to time with simple harmonic motion. To find the spring constant, I used hooke's law and compared different added masses to the stretch from the equilibrium position. When I graphed that, the slope was the spring constant since...
  27. E

    Simple harmonic motion of particles

    Homework Statement Two particles are executing simple harmonic motion of the same amplitude A and frequency ω along the x-axis. Their mean position is separated by distance X0 (X0 > A). If the maximum separation between them is (X0 + A), the phase difference between their motion is My answer...
  28. DeepPatel

    How Do You Convert Pendulum Swings to Frequency and Period?

    Homework Statement A pendulum swings at 70 cycles per minute. a. What is the frequency in Hz? b. What is the period in seconds? Homework Equations T = 1 / f The Attempt at a Solution For part a) Used the answer for part b & I took the equation above, divided 1 by 1.167 cycles/second & got...
  29. RJLiberator

    Mean Input Power & Q value , Damped Harmonic Motion

    Homework Statement Homework EquationsThe Attempt at a Solution I'm working on part a. The numerical value of Q. I have an equation stating that Q = ω_0/ϒ. I don't really know what ϒ is, in other places (http://farside.ph.utexas.edu/teaching/315/Waves/node13.html) it seems like the...
  30. E

    Damped Simple Harmonic Motion: Finding Amplitude Reduction in Carbon Dioxide

    Homework Statement The amplitude of a simple pendulum oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes Law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of...
  31. Elena14

    Phase constant in simple harmonic motion

    I know the phase constant depends upon the choice of the instant t=0. Is it compulsory that the phase constant must be between [0,2π] ? I know that after 2π the motion will repeat itself so it will not really matter, but what is the conventional way to write the phase constant in the general...
  32. P

    Equation for underdamped harmonic motion

    I found an explanation for the equation of under damped harmonic motion, x(t) = C cos(wt) + D sin(wt), but I was wondering if someone could further explain why: - "However, if you assume the function x(t) is real, then they are related as A = B - why is (A-B) is imaginary
  33. C

    Rod rotating about pivot with spring

    Homework Statement Consider the following classic problem: we have a rod in the vertical position with a pivot at its midpoint and a spring attached to the bottom of the rod, perpendicular to the rod. The is rotated through a small angle theta to the vertical, and released. Find the period of...
  34. S

    Simple Harmonic Motion equation rearrangement?

    Homework Statement Hello! I have a physics homework question I just need help at! What I am supposed to do is calculate the value for free-fall acceleration, ag, for each of my trials that I did in my lab. I supposed to use the equation for the period of the simple pendulum, T=2π√l/g, but I...
  35. S

    Equation for Simple Harmonic Motion?

    In Simple Harmonic Motion, can (k/m) = ω2 be expressed for all SHMs or only the ones in which the mass due to which the SHM is being executed is performing a circular motion? Since for example, in the case of spring, there is no circular motion involved, so omega should not be defined for...
  36. O

    Simple Harmonic Motion - Determine quadrant for phase angle.

    Homework Statement When completing this problem I am able to find a value for the phase angle but am unsure of how to find the quadrant for the phase angle therefore unable to get the correct phase angle. Homework Equations Provided in the question: x = xmcos(wt+ phi) The Attempt at a...
  37. J

    Finding time in a simple harmonic motion

    Homework Statement I seem to have problems finding time in SHM. To find the time after projection, I know that either x=asinωt or x=acosωt needs to be used, so since R is projected away from O, it means that it is moving towards the equilibrium position, therefore I used x=acosωt to find the...
  38. Lito

    Harmonic motion- Two springs, One mass

    Homework Statement Two springs each have spring constant k and equilibrium length ℓ. They are both stretched a distance ℓ and then attached to a mass m and two walls (which are 4 ℓ apart). At a given instant, the right spring constant is somehow magically changed to 3k (the relaxed length...
  39. tridianprime

    Simple Harmonic Motion Average Velocity

    Homework Statement At time t = 0, a point starts oscillating on the x - axis according to the law x = a sin(ωt). Find the average velocity vector projection (I assume it means magnitude based on previous questions in the book). Homework Equations The Attempt at a Solution I knew that the...
  40. J

    How Does Laplace Transform Solve the Harmonic Motion Differential Equation?

    (2.) Let the differential equation ¨x + 2 ˙x + 2x = 6 sin(t)U(t − 3π/2) , x(0) = 2, x˙(0) = 2 Solve for the position function x(t) using the Laplace transform:
  41. Q

    Spring constant of object in simple harmonic motion

    Homework Statement A 15.0-N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as a function of time t is given by y(t)=4.50 cos[(19.5s−1)t−π/8] in centimeters. What is the spring constant of the spring? Homework Equations y...
  42. PhotonSSBM

    A charge experiencing simple harmonic motion

    Homework Statement Two positive charges +Q are held fixed a distance apart. A particle of negative charge -q and mass m is placed midway between them, then is given a small displacement x perpendicular to the line joining them and released. Show that the particle describes simple harmonic...
  43. A

    Simple harmonic motion: mass on a spring is hit by a bullet

    Homework Statement A 4.0kg block is suspended from a spring with force constant of 500N/m. A 50g bullet is fired into the block from directly below with a speed of 150m/s and is imbedded in the block. Find the amplitude of the resulting simple harmonic motion. Homework Equations F=-kx...
  44. Lana Elcic

    How Do You Calculate the Period of Oscillation for a Mass on a Spring?

    Homework Statement A 775 g mass is hung on a spring. As a result the spring stretches 20.5 cm. If the object is then pulled an additional 3.0 cm downward and released, what is the period of the resulting oscillation? Homework Equations T = 2pi sqr root(m/k) Hooke's Law Fs=kx The Attempt at a...
  45. Tzabcan

    Simple harmonic motion - initial acceleration

    Homework Statement To work out the intial acceleration, do we just use the equation: So at t = 0 We eliminate the wt inside the bracket, and are left with Aω^(2)sin(Φ + π) Homework EquationsThe Attempt at a Solution The part which I'm not so sure on, is if i have values for Φ, do i...
  46. AsadaShino92

    How Do You Calculate the Damping Coefficient in a Mass-Spring System?

    Homework Statement An object of mass 0.2kg is hung from a spring whose spring constant is 80N/m. The object is subject to a resistive force given by -bv, where v is it's velocity in meters per second. If the damped frequency is √(3)/2 of the undamped frequency, what is the value of b...
  47. Z

    Calculating Amplitude of a Harmonic Motion System with Added Mass

    Homework Statement A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is oscillating on a frictionless, horizontal surface with an amplitude of 2.00 m. A 6.00-kg object is dropped vertically on top of the 4.00-kg object as it passes through its equilibrium...
  48. R

    Optimizing Damping Time: Which Application Would Benefit Most?

    Homework Statement "Which of the following applications would have the most benefit from a short damping time?" a. bathroom scale b. child jolly jumper c. suspension on passenger car d. suspension on race car Homework EquationsThe Attempt at a Solution Im assuming that both A and D should be...
  49. L

    Simple Harmonic Motion - bungee jumping

    Homework Statement A woman bungee-jumper of mass 50 kg is attached to an elastic rope of natural length 15 m. The rope behaves like a spring of spring constant k = 220 N/m. The other end of the spring is attached to a high bridge. The woman jumps from the bridge. a) Determine how far below...
  50. **Mariam**

    Work and energy in simple harmonic motion concept

    Homework Statement Is the statement cirrect: "the rate at which a wave transfers energy depends on the amplitude at which the particles of the medium are vibrating." And does the energy=A^2 ? Homework Equations E (proportional) A^2 The Attempt at a Solution For the statement I am about...
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