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. S

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

    been working on this for a long time, haven't got far, keep getting a negative mass! Homework Statement A 440 g block on a frictionless surface is attached to a rather limp spring of constant k = 8.7 N/m. A second block rests on the first, and the whole system executes simple harmonic...
  2. S

    Simple harmonic motion, finding displacement given time

    Homework Statement mass = 1.8kg given equation in problem x(t) = (7.40cm)cos[(4.16s^-1)t - 2.42] *when i tried solving i converted 7.40cm to 0.074m find the position of the mass at t = 1.00s Homework Equations x(t) = (7.40cm)cos[(4.16s^-1)t - 2.42] The Attempt at a Solution...
  3. 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 =...
  4. P

    Another simple harmonic motion

    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...
  5. P

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

    Homework Statement A 15.8 kg block and a 31.6 kg block are resting on a horizontal frictionless surface. Between the two is squeezed a spring (spring constant = 1868 N/m). The spring is compressed by 0.152 m from its unstrained length and is not attached permanently to either block. With...
  6. I

    Simple Harmonic Motion, Finding Time

    [SOLVED] Simple Harmonic Motion, Finding Time Homework Statement A 0.400 kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.0 cm. Calculate the time interval required for the object to move from x = 0 to x = 4.00...
  7. S

    Solving Simple Harmonic Motion Problems

    [SOLVED] Simple Harmonic Homework Statement A 1.00 kg object is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 19.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object...
  8. 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...
  9. S

    Simple Harmonic Motion (Mass on a Spring)

    [SOLVED] Simple Harmonic Motion (Mass on a Spring) Homework Statement A solid cylinder of mass M= 10.8 kg is attached to a horizontal massless spring so that it can roll without slipping along a horizontal surface, as shown in the Figure. The force constant of the spring is k= 346 N/m. The...
  10. B

    Simple Harmonic Motion of a Pendulum

    Homework Statement What is the amplitude of a pendulum whose angle is given by (.10 rad)cos(5t + pi) where t is in sec. Homework Equations s(t)=Acos(omega*t+phase constant) Theta(t)=thetamax*cos(omega*t+phase constant) The Attempt at a Solution I'm not quite sure if I did this...
  11. B

    Simple Harmonic Motion question

    [SOLVED] Simple Harmonic Motion question Homework Statement A 0.27 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by the following equation. x = (15 cm)cos[(5 rad/s)t + /2 rad)] (a) What is the...
  12. K

    Energy in simple harmonic motion

    Homework Statement This is my first post here. I'm particularly unsure about b(ii) Thanks for any and all replies! I apologize in advance if I haven't used the correct conventions, but I hope that this is legible. I will learn the correct conventions for future posts but was pressed...
  13. U

    Solving for Simple Harmonic Motion Phase Angle

    Homework Statement A block, attached to a spring, moves in Simple Harmonic Motion on a horizontal frictionless table. The displacement from equilibrium is given by x = xm cos (ω t + φ ) where x is positive to the right of the equilibrium position. The frequency of the motion is 3.10 Hz and...
  14. I

    Simple Harmonic Motion of a wave

    [SOLVED] Simple Harmonic Motion Homework Statement A cheerleader waves her pom-pom in simple harmonic motion with an amplitude of 18.0 cm and a frequency of 0.850 Hz. Find (a) the maximum magnitude of the acceleration and of the velocity; (b) the acceleration and speed when the pom-pom's...
  15. X

    Simple harmonic motion and friction

    Homework Statement A large block P executes horizontal simple harmonic motion by sliding across a frictionless surface with a frequency f = 1.5 Hz. Block B rests on it, and the coefficient of static friction between the two is \mu_s=0.60. What maximum amplitude of oscillation can the system...
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. 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...
  21. 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...
  22. 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...
  23. 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...
  24. 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}=...
  25. ~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...
  26. 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...
  27. 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...
  28. 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...
  29. 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...
  30. ~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...
  31. ~christina~

    Motion of object (simple harmonic motion?)

    Homework Statement A ball dropped from height 4.00m makes an ellastic collision with the ground. Assuming no mechanical energy is lost to air resistance. a) show that the motion is periodic b) determine period of motion c) is the motion simple harmonic? Homework Equations...
  32. L

    Simple Harmonic Motion in daily life

    Do you think that the daily movement of a student from home to university then again from university to home is an example of simple harmonic motion ? Please give the arguments in support of your point of view.
  33. J

    Question abou Simple Harmonic Motion

    Homework Statement A spring mass system has the following parameters: Mass m=1 kg, spring constant k=100 N/m. The oscillations are started by initially displacing the mass so that the spring is compressed by 0.5 cm and releasing it from rest. What is the speed of the mass (in m/s) when it...
  34. L

    SHM - Finding Distance and Direction of Oscillating Particles

    SHM - Simple Harmonic Motion Question Homework Statement Two particles oscillate in SHM along a common straight-line segment of length A. Each particle has a period of 1.5s, but they differ in phase by π/6 rad. a. How far apart are they 9in terms of A) 0.50s after the lagging particle...
  35. S

    Average Kinetic & Potential Energy in Simple Harmonic Motion

    in SHM average K.E when done w.r.t to time is equal to average potential energy calculated w.r.t to time. but today in class when my sir asked me to to prove average K.e = average P.E I just tried integrating it w.r.t to displacement and then divided it with A , I thought this gives us av...
  36. D

    Simple Harmonic Motion - Floating Object

    [SOLVED] Simple Harmonic Motion - Floating Object Homework Statement The problem states that an object is pushed down and released. It is floating. The density is P(block) and the area is A and its height is h The fluid's density is P(fluid) The Problem asks to show that it executes...
  37. S

    Why Does Adding 2π to the Phase Angle Yield Equivalent Solutions in SHM?

    In simple harmonic motion example there is a question velocity max is given velocity at time = 0 is given (which is not equal to maximum velocity --> not at equilibrium point at time=0) graph is also given of the velocity function IT asks to find the phase angle in the solution they...
  38. V

    Simple Harmonic Motion of a body

    Homework Statement A body is in simple harmonic motion of amplitude 0.50m and period 4pie seconds. What is the speed of the body when the displacement of the body is 0.30 m? Homework Equations Would it be x=Acos2(pie)ft ? The Attempt at a Solution I tried substituing in x=...
  39. M

    Derivation of Simple Harmonic Motion for a Spherical Bowl

    Problem: Prove that it is valid to model a particle in a smooth hemispherical bowl as a simple pendulum, provided its maximum displacement is small. Answer: Usually, a FBD is used along with Newton's 2nd, and then the small angle approximation is used twice (once for siintheta in the weight...
  40. M

    Simple harmonic motion of a spring

    Homework Statement A horizontal plank (m = 2.0 kg, L = 1.0 m) is pivoted at one end. A spring (k = 1.0 x 10 3 N/m) is attached at the other end, as shown in the figure. Find the angular frequency (in rad/s) for small oscillations Homework Equations w = (mgd/I)^0.5 I= 1/3 ML^2...
  41. M

    Energy Problem involving simple harmonic motion

    Homework Statement The motion of a particle is described by x = 10 sin (piet +pie/2 ). At what time ( in second ) is the potential energy equal to the kinetic energy ? Homework Equations KE = 1/2 mv^2 PE=1/2 Kx^2 The Attempt at a Solution V=pie10cos(piet + pie/3) V^2 = pie^2...
  42. L

    Understanding Simple Harmonic Motion: Equations and Parameters Explained

    I'm confused on part of an AP Physics lab on "Simple Harmonic Motion from a Force Perspective." Using a hanging spring & mass, motion detector, and CBL unit/Ti-83 graphing calculator, we used the calculator's graphs to create equations that included the amplitude, angular frequency, the phase...
  43. C

    Energy in Simple Harmonic Motion

    A 1.3 kg object oscillates with simple harmonic motion on a spring of force constant 410.0 N/m. The maximum speed is 0.7 m/s. What is the total energy of the object and the spring? Do I just set it up like this: 1/2*410*x^2=1/2*1.3*.7^2 to get the max x Then do I just add them up
  44. V

    Simple Harmonic Motion of an earthquake

    [SOLVED] Simple Harmonic Motion Homework Statement Four people, each with mass of 71.1 kg, are in a car with a mass of 1180 kg. An earthquake strikes. The vertical oscillations of the ground surface make the car bounce up and down on its suspension springs, but the driver manages to pull of...
  45. J

    Simple Harmonic Motion of an ideal spring

    Homework Statement An ideal spring has a spring constant k = 29 N/m. The spring is suspended vertically. A 1.4 kg body is attached to the unstretched spring and released. It then performs oscillations. (a) What is the magnitude of the acceleration of the body when the extension of the...
  46. T

    Simple Harmonic Motion and parallel-axis-theorem

    Hello, I have problems solving the following two problems: 1)You measure the period of a physical pendulum about one pivot point to be T. Then you find another pivot point on the opposite side of the center of mass that gives the same period. The two points are separated by a distance L. Use...
  47. A

    Springs and simple harmonic motion

    Homework Statement If the initial period is 3.0 s and the mass is reduced to 1/3 of its initial value, what is the new period?Homework Equations Possibly T=2pi*squareroot(m/k)The Attempt at a Solution The solution is something close to 1.73. I have no idea what equation to use, even. Any...
  48. D

    Simple Harmonic Motion Reference Circle

    Homework Statement Through simple harmonic motion produced on a trampoline Ivan ossilates freely, with a period of 0.85s. On a reference circle show Ivans position after 1/8th of a cycle. Label (and solve) the distance of this position from the equilibrium position.(Max displacement is...
  49. C

    Simple Harmonic Motion and Wave Motion

    Hi, I was wondering if anyone could explain Simple Harmonic Motion. My physics teacher has tried and I have read the parts in the book, but I am still confused. I know how to find the amplitude from the standard form equations, but I really just don't understand how to get the period and...
  50. A

    Simple Harmonic Motion - Period (T)

    [SOLVED] Simple Harmonic Motion - Period (T) 1. A pendulum oscillates with a period T. If both the mass of the bob and the length of the pendulum are doubled, the new period will be _____. 2. T = 2(pi) x rad (k/m) 3. Since L is not a part of the equation, it shouldn't affect...
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