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. Y

    Phase space diagram for a spring in simple harmonic motion

    Homework Statement A mass m = 750 g is connected to a spring with spring constant k = 1.5 N/m. At t = 0 the mass is set into simple harmonic motion (no damping) with the initial conditions represented by the point P in the phase space diagram at the right. **(This phase space diagram has...
  2. F

    Velocity vs time graph simple harmonic motion phase constant

    Homework Statement http://i.imgur.com/u8vUv5a.jpg Find the phase constant. Homework Equations x(t)=Acos(ωt + Φ) v(t)=-Aωsin(ωt + Φ) Vmax = ωA ω=2π/T The Attempt at a Solution ω = 2π/12 = 0.5236 A = 60/0.5236 = 114.59 cm v(0) = -30 = -114.59(0.5236)sinΦ 0.5 = sinΦ Φ = π/6 and 5π/6. Which...
  3. F

    Simple harmonic motion oscillate. What is the total energy

    Homework Statement The position of a 50 g oscillating mass is given by x(t)=(2.0cm)cos(10t−π/4), where t is in s. If necessary, round your answers to three significant figures. Determine: The total energy. Homework Equations T = 2π/w T = 2π√m/k 1/2kA^2 1/2mv^2 1/2kx^2 The Attempt at a Solution...
  4. T

    Simple Harmonic Motion Question

    Homework Statement I have a question about simple harmonic motion: Where it says " if we denote the ratio k/m with the symbol omega squared ... ": I know it says that they chose omega squared to make the solution simpler, but I mean, to me it doesn't really make sense. Omega is associated...
  5. R

    Forced Frequency Homework: Which of These Acts as a Force?

    Homework Statement Which of the following is a forced frequency acting on the oscillations? I. A pendulum skims the surface of a pool of water at the lowest point of motion. II. To keep a bell ringing, a bell ringer pulls on a bell rope. III. A singer shatters a glass. Homework EquationsThe...
  6. P

    Simple harmonic motion period with velocity defined

    Homework Statement A mass m is sliding back and forth in a simple harmonic motion (SHM) with an amplitude A on a horizontal frictionless surface. At a point a distance L away from equilibrium, the speed of the plate is vL (vL is larger than zero). Homework Equations What is the period of the...
  7. J

    Simple Harmonic Motion experiment

    Hi pf. I have a question about an experiment. If you lie a ruler horizontally across two supports (one near each end) and then hang a weight in the middle it will undergo SHM if you pull the mass down. If you move the supports in closer it will oscillate with a higher frequency. I just wanted to...
  8. praveenpandiyan

    Frequency of Resultant Periodic Function from Sum of Three Harmonic Functions

    Homework Statement three harmonic function of frequency p, 2p ,3p were added together. what is the frequency of resultant periodic function? Homework Equations X=Asin(wt) A-amplitude w-frequency X=X1+X2+X3 The Attempt at a Solution need a hint ..
  9. N

    Physics Report Help -- Simple Harmonic motion and Elastic force

    Homework Statement So I have to write a report based on an experiment that I have conducted. I know that my report is connected with Simple Harmonic motion and Elastic force, but I do not know how to describe it in a more efficient/scientific way. Essentially, I am dropping a weight (constant)...
  10. SalfordPhysics

    FORTRN90: Euler Midpoint Method for SHO

    Homework Statement Write a program to simulate motion of simple harmonic oscillator. Initial conditions: Let ω = 1, x(t=0) = 1, v(t=0) = 0. Integrate over 30 seconds in intervals of 0.05s. Homework Equations δ2x / δt2 = -ω2x As set of 2 coupled ODE's; x' = v, v' = -w2x The...
  11. J

    Simple Harmonic Motion of bobble toy

    *note: my previous thread will be deleted because I didn't include relevant equations + I put two unrelated problems in the same thread. 1. Homework Statement A cat bobble head doll consists of a weighted head on top of a spring. When the head hangs straight sown in equilibrium, it is observed...
  12. E

    Simple Harmonic Motion and speed of mass

    Homework Statement [/B] A mass-spring system is oscillating with an amplitude of 10.0 cm. What is the speed of the mass at a location where the kinetic energy of the mass and the potential energy of the spring are equal? I want to know if it's possible to solve for just a number, that is, not...
  13. I

    Simple Harmonic Motion experiment help

    I did an experiment at school, and the experiment SET UP that i did is basically shown in the word attachment link. http://www.schoolphysics.co.uk/age16-19/Mechanics/Statics/experiments/bending_of_a_beam.doc. I have two questions! Question 1:when i did the experiment, I found that with a...
  14. A

    Find how far apart are the particles from each other

    Homework Statement Two particles oscillate in simple harmonic motion with amplitude A, about the centre of a common straight line of length 2A. Each particle has a period of 3.3 s, and their phase constants differ by π/9 rad. (Assume the lagging particle starts at +A. Also assume that the...
  15. S

    Why is the motion of a piston considered to be simple harmonic motion?

    I know this is simple, but I don't fully understand why the motion of a piston is considered to be simple harmonic? Wouldn't the piston and connecting rod have mass?
  16. A

    Simple Harmonic Motion and angular frequency

    Homework Statement A horizontal plank of mass m and length L is pivoted at one end. The plank's other end is supported by a spring of force constant k (see the figure below). The plank is displaced by a small angle θ from its horizontal equilibrium position and released. Find the angular...
  17. F

    How to find phi in simple harmonic motion

    Given a position vs time graph of simple harmonic motion of an object and using the equation x(t) = xo = A sin (ωt +Φ), how am I supposed to find Φ? I can easily find A and the period (T). I also know T = 2 pi / ω, so I can find ω. But I don't know x(t) and t. I tried finding random points in...
  18. ZARATHUSTRA

    Understanding the Equation of Motion for Simple Harmonic Motion

    For one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, could be obtained by means of Newton's second law and Hooke's law and i don't get this part which...
  19. pyman999

    Simple harmonic motion acceleration

    Homework Statement Homework Equations acceleration = -(2*pi*f)^2 * x, where f is the frequency and x is the displacement from equilibrium. The Attempt at a Solution I thought the acceleration would be greatest when the displacement from equilibrium is greatest, so at point P, but the answer...
  20. pyman999

    Simple harmonic motion question

    Homework Statement http://puu.sh/cAjmp/14ba3df23a.jpg Homework Equations Acceleration at any instant: -(2*pi*f)^2 * x, where x is displacement from equilibrium and f is frequency. The Attempt at a Solution Firstly, I know it can't be D as acceleration would increase as potential energy...
  21. Misheel

    Oscillation Problem: Find Period and Potential Energy

    Homework Statement mass "m" object is located near the origin of the coordinate system. External force was exerted on the object depending on the coordinate by the formula of Fx=-4*sin(3*pi*x). Find the short oscillation period, and the potential energy depending on the coordinate. Homework...
  22. T

    About velocity equation in simple harmonic motion

    Homework Statement Actually this is not a problem. This is about something i couldn't understand. Homework Equations where wt equals θ The Attempt at a Solution I can understand that x=r.cosθ it is obvious. But i can't understand why Vx=-V.sin(w.t) When i take a triangle from that...
  23. A

    Simple Harmonic Motion equation question: which length and why

    Homework Statement I solved this physics question, but I am unclear about why Amplitude was the amount the spring was stretched by (which should be the new equilibrium point), instead of the amount the person pulled the mass down by (which should be the amplitude). Can anyone help? On your...
  24. sergiokapone

    Harmonic oscillations of the electromechanical system (normal modes)

    Homework Statement http://imagizer.imageshack.us/v2/275x215q90/661/kIVMcC.png Mathematical pendulum is the part of the oscillating circuit. The system is in a constant uniform magnetic field. Oscillations is small. Find the normal modes of oscilations. Homework Equations ## \begin{cases}...
  25. B

    Simple Harmonic Motion Pendulum problem

    Homework Statement A simple pendulum of length =30.0cm is released from rest from an angle of θ=10.0∘ to the vertical. Assuming that the pendulum undergoes simple harmonic motion, find its maximum speed. Source: https://isaacphysics.org/questions/accuracy_shm_pendulum_num Homework Equations a)...
  26. S

    Calculating Mass of a Block in SHM with Given Parameters

    Homework Statement A block attached to a horizontal spring of force constant 75 N/m undergoes SHM with an amplitude of 0.15 m. If the speed of the mass is 1.7 m/s when the displacement is 0.12 m from the equilibrium position, what is the mass of the block? k = 75 N v = 1.7m/s @ 0.12m...
  27. Subhadeep Dey

    Applications of Damped Oscillation (in Vibrations): Researching for a Paper

    I've been researching on Damped Oscillation (in vibrations) for a few days for a research paper, however I couldn't find any applications. I would be very thankful if anyone can tell me about its applications.
  28. J

    Interpreting Simple Harmonic Motion Graphs

    Homework Statement Explain the shape of the velocity-displacement and acceleration-displacement graphs for an object undergoing simple harmonic motion. The graph is attached to this thread Homework Equations v = wsqrt(A^2-x^2) where w = angular frequency, A = amplitude and x = displacement...
  29. A

    Understanding Simple Harmonic Motion: Explained in Simple Terms

  30. A

    Simple Harmonic Motion Guitar String Question

    Homework Statement Question: "The midpoint of a guitar string oscillates with an amplitude of 2.24mm with a frequency of 400Hz. Calculate: i) The maximum speed at this point ii) The maximum acceleration of the string at this point" Homework Equations Suitable formulas: x=Asin(2*pi*f*t) ...
  31. P

    Simple Harmonic Motion: Why is acceleration positive at maximum displacement?

    For example, I have a pendulum with amplitude of 2m, when the pendulum is at a displacement of 2m, wouldn't the acceleration be negative as the restoring force is acting towards equilibrium? The equation I am taught is that maximum acceleration is (2*pi*frequency)^2 * amplitude, which is a...
  32. T

    Simple harmonic motion platform

    1. A platform is executing simple harmonic motion in a vertical direction with an amplitude of 5 cm and a frequency of 10/pi vibrations per second. a block is placed on the platform at the lowest point of its path. a) at what point will the block leave the platform? b)how far will the block...
  33. L

    Gravitational force in simple harmonic motion

    Homework Statement I am trying to derive the formula for simple harmonic motion of a mass hanging on a spring. I understand the derivation for the situation when the mass and the spring are on an horizontal table. Then I go about deriving the same formula for the situation when a mass is...
  34. H

    Simple Harmonic Motion Pendulum, can we use PE=1/2kAmplitude^2?

    I was wondering if we can somehow use the formula Potential Energy = 1/2K(x(x=Amplitude))^2 for a pendulum if we are only given the angle of displacement? Would the problems normally just say the PE at the top of the pendulum is such and such, please find max Velocity, Or also the max...
  35. A

    Under-damped simple harmonic motion solution derivation

    I have learned in 1st year that the under-damped simple harmonic motion can be described by the differential equation m \frac {d^2 x} {dt^2} + b \frac {dx} {dt} + kx = 0 where m is the mass, b is the constant of linear drag and k is the spring constant But the derivation is skipped...
  36. N

    Is the propagation of a wave simple harmonic motion?

    Is the propagation of a wave simple harmonic motion? Simple harmonic motion is defined when the restoring force is proportional to the displacement. Hooke's Law F = -kx is an example. However at my level of understanding I have not yet read about the relationship between forces and waves and...
  37. 2

    Why is a pendulum only simple harmonic motion for small angles?

    Homework Statement Hi all! I'm slightly confused about pendulums and simple harmonic motion. In my textbook, it says that a pendulum only exhibits simple harmonic motion when the angle is small (<10 degrees). I was wondering why this is, using equations if possible. Without the math, I think...
  38. G

    Simple harmonic motion and circular motion

    why simple harmonic motion is projected as or compared with uniform circular motion ?
  39. G

    Simple harmonic motion and positive constant w^2?

    in defining the Equation of simple harmonic motion taking origin as fixed point and the line of motion as x axis. a(acceleration) = - w^2 * x. where w^2 is positive constant. what is the reason behind taking square of w as constant not just w?
  40. K

    Condition of simple harmonic motion

    Homework Statement I was told that for an object to execute SHM, the x (distance displaced from the spring) can't be greater than e . Why is this so? i can't understand. can someone explain please? Homework Equations The Attempt at a Solution
  41. D

    Show that simple harmonic motion occurs

    Homework Statement A wheel with moment of inertia I. A mass of M is connected to a belt and runs over the wheel with radius R and connected to a spring with a stiffness of k which is connected to the ground. Show that if the mass is pulled down with a force of F and released the system will...
  42. K

    Simple harmonic motion (direction of acceleration)

    Homework Statement my question is on part d, (iv), i assume this is a pendulum experiment. the equlibrium position is at 30cm. then the negative amplitude should be located at 24.0cm. the particle moved from 24.0cm to 36.0cm. the acceleration is always acted towards the equlibrium position. so...
  43. A

    Introductory Simple Harmonic Motion Problem

    Q: When a sound wave with a certain intensity is detected by the tympanic membrane, the amplitude of the resultant motion is 1.0 nm (1.0 x 10-9 m). If the frequency of the sound is 600 Hz, what is the maximum speed of the membrane oscillation? My answer: 1)Vmax = wA (where w= angular velocity)...
  44. M

    Show that the simple harmonic motion has a period

    A mass m slides on a frictionless horizontal surface, connected to two springs, as shown below. If the force have constants K1 and K2 , show that the simple harmonic sliding motion has period. T= 2 Pie (Square Root X m { K1+K2/K1K2}) So far I have →From equation T= 2Pie{SquareRoot(m/k)...
  45. C

    Relationship between Simple Harmonic Motion Equation and Wave Equation

    I am very familiar with the equation: $$f(t)=Asin(ωt+ϕ)$$ Used to describe the instantaneous value f(t) of a wave with amplitude A, frequency ω, and phase shift ϕ at time t. This equation is very intuitive to understand: As t increases the value within the sin operator will increase from ϕ...
  46. J

    Changing equilibrium point in damped simple harmonic motion

    Hi I have a damped simple harmonic motion model and I am altering the input force along with spring constant and damping constant. I can change the damping and spring constant to allow it to oscillate for few seconds before it stops at 0. What parameters do I need to change to alter the...
  47. S

    Simple Harmonic Motion Pendulum

    Homework Statement A small sphere with mass m is attached to a massless rod of length L that is pivoted at the top, forming a simple pendulum. The pendulum is pulled to one side so that the rod is at an angle θ from the vertical, and released from rest. When the pendulum rod is...
  48. J

    Instantaneous response of damped simple harmonic motion

    Hi I am trying to model SHM in Simulink as shown here: http://pundit.pratt.duke.edu/wiki/Simulink/Tutorials/DiffEq I have tried using different values of spring constant and damping to get instant response to the input force. I am measuring the displacement calculated by SHM. The force changes...
  49. C

    Total distance in simple harmonic motion

    Homework Statement A mass oscillates along the x-axis in simple harmonic motion. It goes through 200 cycles in 10 seconds and its vibrational amplitude is 0.020 m. What is the frequency, in hertz, and the total distance traveled, in meters, by the mass in the 200 cycles? Homework...
  50. Q

    Simple Harmonic Motion Displacement

    Homework Statement A particle is in simple harmonic motion with period T and with position as a function of time given by x(t) = A cos(wt+ø). At time t = 0 the particle is at x = A/2 with positive velocity. The next time it is at the same position is ___? Homework Equations...
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