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. 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...
  2. 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...
  3. 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...
  4. S

    Is a Vertically Hung Spring Mass System SHM?

    In an SHM, the only force that should be acting, that is the net force should be the restoring force F, by definition... F = -kx For example there is a massless spring of spring constant k attached to the ceiling and there is a body of mass m hung at it and avoiding all kinds of friction...
  5. 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...
  6. 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...
  7. 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...
  8. tridianprime

    Simple Harmonic Motion Average Velocity

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  9. B

    Amplitude vs Location when KE=PE?

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  10. A

    Determining the Spring Constant for a Pendulum with a Spring-Loaded Launcher

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  11. **Mariam**

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  12. 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...
  13. PhotonSSBM

    A charge experiencing simple harmonic motion

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  14. A

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

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  15. 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...
  16. Tzabcan

    Simple harmonic motion - initial acceleration

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  17. 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...
  18. Alettix

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  19. 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...
  20. **Mariam**

    Work and energy in simple harmonic motion concept

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  21. N

    Simple harmonic motion problem

    I translated it, so the notation may not be so great. You have a vertical spring with a spring constant of 16 N.m^-1, we attach to its lower end a body with a mass of 0,4 KG and form a system which oscillates on a straight line with length of 8cm, we assume that at the start of the time, the...
  22. L

    Simple harmonic motion - answer slightly off

    Homework Statement A 4.00kg block is suspended from a spring with k = 500N/m. A 50.0g bullet is fired into the block from directly below with a speed of 125m/s and becomes embedded in the block. a) Find the amplitude of the resulting SHM. b) What percentage of the original kinetic energy of...
  23. D

    Need help in deciding what to research for physics project

    Hello enlighted people of this forum. I'm an undergraduate from a university in Colombia, my subject of study is software engineering but I have a class which is named "Physics 2", this class introduces the subjects of simple harmonic motion(pendulum, sound waves, etc), electric fields, Gauss's...
  24. D

    Simple Harmonic Motion and phase constant

    A simple harmonic oscillator consists of a block of mass 45 g attached to a spring of spring constant 240 N/m, oscillating on a frictionless surface. If the block is displaced 3.5 cm from its equilibrium position and released so that its initial velocity is zero, what is the phase constant, φ ...
  25. M

    Simple Harmonic Motion of a 12kg mass

    A 12kg mass undergoes simple harmonic motion with an amplitude of 10cm. If the force constant for the spring is 320N/m: a) Calculate the total energy of the mass spring system. Et=½kA^2 =½(320N/m)(0.1m)^2 =1.6 Jb) Calculate the maximum speed of the mass. Et=½mv^2 + ½kx^2 1.6 J = ½(12kg)v^2...
  26. B

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    Homework Statement One end of a spring is attached to a wall to a block of mass X= 2kg (on a frictionless horizontal table). Another mass M of 150g moving at a speed of 7m/s collides (inelastic). This takes 0.4s to compress the spring to its max compression. I have to find the max force of...
  27. Alettix

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  28. E

    Difference between X and Amplitude (Simple Harmonic Motion)?

    V=Vo √1-(x^2/a^2) X is the distance of the spring's stretch, but how would you rearrange the equation if you are looking for Amplitude? They both use the same units (meters) as far as I am concerned. Help would be appreciated, thanks; I am still a beginner with Physics.
  29. Samurai44

    Simple harmonic motion energy question

    Homework Statement Can I get help in part (b) of this question ? Homework Equations KE=1/2 m v2 v= (2π f )√(A2 - x2) The Attempt at a Solution I substituted the second equation into first one, so i got KE= 1/2 m (2π f )2 (A2 - x2) but then couldn't complete
  30. M

    Calculating the Period of a Simple Harmonic Oscillator with a Pivoted Metal Rod

    Homework Statement A L = 1.48 m long metal rod is pivoted from a point one third of the way along its length. The rod has a mass of 0.208 kg. What period will the rod oscillate with when released from a small angle? Homework Equations T = 2 \pi \sqrt{\frac{L}{g}} The Attempt at a...
  31. L

    Angular Simple Harmonic Motion

    1. The balance spring of a watch is a hoop 1.2 cm in diameter, with a mass of 0.65 g. If the watch is running 45 seconds per day too fast, by what percentage should the rotational inertia of the hoop be changed? 2. Homework Equations : I = mR^2 Ia = -k(theta) x(t) = Xm Cos(wt + @) (just using @...
  32. L

    Simple Harmonic Motion Question (Springs)

    A 350-g mass is attached to a spring whose spring constant is 64 N/m. Its maximum acceleration is 5.3 m/s2. What is its maximum speed? So, i had a go at the question which basically required the knowledge that maximum acceleration occurs when displacement is maximum and maximum velocity occurs...
  33. AdityaDev

    A particle of mass m moves in a one dimensional potential

    1.The problem, statement, all variables and given/known data A particle of mass m moves in a one dimensional potential U(x)=A|x|3, where A is a constant. The time period depends on the total energy E according to the relation T=E-1/k Then find the value of k. 2. Homework Equations V=dx/dt...
  34. S

    What Is the Speed of a Mass at Equilibrium in Simple Harmonic Motion?

    Homework Statement A 1.0 Kg mass is attached to the end of a vertical ideal spring with a force constant of 400 N/m. The mass is set in simple harmonic motion with an amplitude of 10 cm. The speed of the 1.0 kg mass at the equilibrium position is. A. 2 m/s B. 4 m/s C. 20 m/s D. 40 m/s E. 200...
  35. Calpalned

    Understanding Simple Harmonic Motion: Homework Equations and Graph Analysis

    Homework Statement My textbook states that for simple harmonic motion, the sinusoidal graph of the x (displacement) as a function of time can be created using the "Equation of motion". Homework Equations The equation of motion ##A \cos (\omega t + \phi)## The Attempt at a Solution I know...
  36. T

    Simple Harmonic Motion with Damping and Driving

    Hello, I was asked by my professor today to graph the motion, as well as the energies, of a spring that undergoes driven and/or damped oscillation; however, I was unable to because I do not have a very good idea of how they work. Can someone explain to me, qualitatively, what it means to have a...
  37. M

    Simple Harmonic Motion: Particle Speed and Acceleration Calculation

    Homework Statement A particle moves with simple harmonic motion in a straight line with amplitude 0.05 m and the 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)] Homework...
  38. S

    Phase Difference with Initial Conditions for SHM

    Homework Statement A mass-spring system with a natural frequency of 3.6 Hz is started in motion with an initial displacement from equilibrium of 6.1 cm and an initial velocity of 0.7 m/s. What is the value of ϕ? (Question aside: Finding the amplitude of the resulting function?) Homework...
  39. L

    What is the direction of friction on a plate on two rotating wheels?

    Homework Statement A uniform plate of mass M stays horizontally and symmetrically on two wheels rotating in opposite directions. The separation between the wheels is L. The friction coefficient between each wheel and the plate is N. Find the time period of oscillation of the plate if it is...
  40. kate Co

    Simple Harmonic Motion Question?

    Homework Statement A 0.500Kg object is undergoing simple harmonic motion at the end of a horizontal spring with force constant k=300N/m. When the object is 0.012m from the equilibrium position, it is observed to have a speed of 0.300m/s. What is: a) The total energy of the object at any point...
  41. P

    Simple Harmonic Motion problem with spring mass system

    Homework Statement A 50g mass is attached to a spring and undergoes simple harmonic motion. It's maximum acceleration is 15m/s and maximum speed is 3.5m/s. Determine a)angular frequency, b) spring constant, c) amplitude. Homework Equations ω = √k/m X(t) = A*cos(ωt + ∅) The Attempt at a...
  42. T

    Vertical Simple Harmonic Motion

    Homework Statement Homework EquationsThe Attempt at a Solution Suppose mass of platform is ##M_1## and that of coin is ##M_2## . The normal force between them is N . EOM for platform (mass M1) = ##-kx+M_{1}g+N = M_{1}\ddot{x}## EOM for coin(mass M2) = ##M_{2}g-N = M_{1}\ddot{x}## This...
  43. Jediknight

    What is the maximum distance traveled by the block in a vertical spring system?

    Homework Statement The hand in (Figure 1) (a) holds a vertical block-spring system so that the spring is compressed. When the hand let's go, the block, of mass m, descends a distance d in a time interval Δt before reversing direction in (Figure 1) (b). Once the system comes to rest, the...
  44. J

    Simple Harmonic Motion and acceleration

    Hi, I have a few questions relating to the equation for maximum acceleration for SHM: amax = A (2 x pi x f)^2 where amax = max. acceleration, A = amplitude, f = frequency. How are these variables supposed to be interpreted when you relate them to each other. For example, is A inversely...
  45. A

    Simple Harmonic Motion, Initial Displacement vs Initial Cond

    Hi everybody, I'm writing an exploration on the mathematics of simple harmonic motion and I stumbled across something I fail to understand in one of my resources (http://tutorial.math.lamar.edu/Classes/DE/Vibrations.aspx). In the example the author uses toward the end of the resource, the...
  46. Jediknight

    Simple Harmonic Easy Qualitve problem, something I'm not getting

    Homework Statement Which of these forces could result in simple harmonic motion F(x)=−9(x−7)3 F(x)=−9x+7 F(x)=−9x3 F(x)=−9x F(x)=9x F(x)=9x3 9x3 is 9x^3, same with itsopposite Homework Equations F=kx, the definition of shm The Attempt at a Solution I figured -9x and 9x were the only...
  47. C

    Can x=8sin2t+6cos2t be proven as S.H.M. using a second derivative?

    Homework Statement Prove that: x=8sin2t+6cos2t is undergoing S.H.M. (Not too sure about how to prove for solution.) Homework Equations Solution for S.H.M. x=asin(nt+α) is \frac{d^{2}x}{dy^{2}}=-n^2xThe Attempt at a Solution...
  48. S

    Simple Harmonic Motion oscillation amplitude

    Homework Statement A mass on a spring has an angular oscillation frequency of 2.56 rad/s. The spring constant is 27.2 N/m, and the system's kinetic energy is 4.16 J when t = 1.56 s. What is the oscillation amplitude? Assume that the mass is at its equilibrium position when t = 0.a. 63.1 cm b...
  49. P

    Simple Harmonic Motion & Pendulum Problem

    Homework Statement What length must the pendulum be changed to in order to show the correct time? L=0.5m After 12hours the clock is behind by 30minutes. Homework Equations w=sqrt(g/L) w=2πf The Attempt at a Solution I thought if I set the frequency equal to 1Hz and solved for length it would...
  50. S

    Does Initial Spring Tension Affect SHM Frequency?

    Find the spring constant by timing simple harmonic motion. I have done a Hooke's law experiment already and found out about initial tension. What I learned was: force ≠ spring constant x displacement force = initial tension + (spring constant x displacement) So using F=kx would not give an...
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