Simple harmonic motion Definition and 916 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. Amith2006

    Calculating Time Period of Simple Pendulum with Charged Capacitor | SHM Homework

    Homework Statement # A simple pendulum having charge q, mass m and effective length l is suspended from a rigid support between the plates of a charged capacitor whose plates are kept vertical. What is the time period of oscillation of the pendulum? Homework Equations Time period =...
  2. K

    Spring Simple Harmonic Motion problem

    Hey, my teacher gave me these two problems for Homework and me nor anybody else in my class has no idea how to do them, any help would be greatly appreciated. 1. a 15.0kg block rests on a horizontal table and is attached to one end of a massless, horizontal spring. By pulling horizontally on...
  3. F

    Simple Harmonic Motion of mechanical bull

    Homework Statement While visiting friends at Cal State Chico, you pay a visit to the Crazy Horse Saloon. This fine establishment features a 200- kg mechanical bucking bull that has a mechanism that makes it move vertically in simple harmonic motion. Whether the “bull” has a rider or not, it...
  4. E

    Simple harmonic motion rope swing problem

    Jane wants to swing on a rope across a river. What minimum speed does she need to make it across, and once she's across, what minimum speed does she need to make it back? Here's what's given: mass = 47 kg horizontal wind - call it F - (opposite to her swing) = 120 N horizontal distance (D) =...
  5. S

    Energy and Simple Harmonic Motion - Part II.

    A horizontal spring is lying on a frictionless surface. One end of the spring is attached to a wall whle the other end is connected to a movable object. The spring and object are compressed by 0.064 m, released from rest, and subsequently oscillate back and forth with an angular frequency of...
  6. S

    Energy and Simple Harmonic Motion.

    A vertical spring with a spring constant of 470 N/m is mounted on the floor. From directly above the spring, which is unstrained, a 0.30 kg block is dropped from rest. It collides with and sticks to the spring, which is compressed by 2.5 cm in bringing the block to a momentary halt. Assuming air...
  7. B

    Simple harmonic motion questions

    A u-tube manometer is half filled with water. The liquid levels are displaced so that one side is higher than the other. The water is then left free to oscillate from side to side. The tube has a cross sectional area of 1.cm^2 and the inital displacement is 0.1m from the rest position, which is...
  8. M

    Simple Harmonic Motion and frequency of vibration

    When a 63 kg person climbs into a 1040 kg car, the car's springs compress vertically by 3.3 cm. What will be the frequency of vibration when the car hits a bump? Ignore damping. Here is the FBD I have drawn: http://img276.imageshack.us/img276/6189/fbdcc2.png Im not even sure if this is...
  9. S

    Understanding the Use of Sin and Cos Formulas in Simple Harmonic Motion

    H, I missed the class so may be asking something really dumb her but have got a test today and want to do well so here goes: in what cases should you use either of these formulas? (we have been told to remember them but not told when either is more relavent that the other, and my book doesn't...
  10. S

    Finding Angular Frequency for Simple Harmonic Motion - Mass and Rod System

    OK, the answer for this problem seems a bit high to me, so I'm going to ask if it all seems alright. You have a 1m rod of no mass, fixed so that it may rotate about it's center. At the top of the rod is a mass m1 (0.5kg), and the bottom is a mass m2 (1.0kg). Find the angular frequency assuming...
  11. R

    Proving v^2 = n^2 (A^2-x^2) from v dv/dx = -n^2x

    hey guys, just hpoping sum1 could point me in the rite direction...i can't wrk out how to proove v^2=n^2 (A^2-x^2) from v dv/dx = -n^2x obviously you hav to integrate...but i don't know how they get the A into the equation?? what i hav tried is intergating both sides with recpect to x...
  12. L

    Calculate Initial Bullet Speed in SHM with Block-Spring System

    My teacher set us a bunch of pendulum/SHM questions, and I managed to crack them all except for this one which has been bothering me: "A 5.4 g bullet is fired horizontally into a 0.50 kg block of wood resting on a frictionless table. The block, which is attached to a horizontal spring...
  13. B

    Understanding Simple Harmonic Motion: Contradicting Acceleration and Velocity

    When observing the acceleration graph of simple harmonic motion we can see that the acceleration is just the opposite of the elongation. Yet we know that the pendulum velocity is increasing when approaching the equilibrium state. Which means that the motion is accelerated altough the sign of the...
  14. A

    Calculating Speed of Simple Harmonic Motion with Initial Displacement

    Please help with the following problem: A 0.1 kg block rests on a level surface and is attached to a horizontally aligned spring with a spring constant of 32 N/m. The block is initially displaced 4 cm from the equilibrium position and then released to set up a simple harmonic motion. A...
  15. Amith2006

    Weakly Damped Harmonic Oscillator: Phase Difference

    Sir, A weakly damped harmonic oscillator is executing resonant oscillations. What is the phase difference between the oscillator and the external periodic force?
  16. D

    Damped Simple Harmonic Motion problem

    I'm having trouble with this problem.The suspension system of a 2100 kg automobile "sags" 7.2 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 35% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock...
  17. S

    Simple Harmonic Motion and Damping

    Textbook Question: Which one of the following terms is used to describe a system in which the degree of damping is just enough to stop the system from oscillating? a) Slightly damped b) Underdamped c) Critically damped d) Overdamped e) Resonance Textbook says that the smallest...
  18. M

    Simple Harmonic Motion of a plank of mass

    I don't understand the solution to the following problem: 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. The moment of inertia of the plank about the pivot is (1/3)m(L^2). The plank is displaced by a small...
  19. C

    Simple Harmonic Motion of a block

    A 0.50 kg block sits on top of a 5.00-kg block that rests on the floor. The larger block is attached to a horizontal spring that has a force constant of 15.0 N/m. It is displaced and undergoes simple harmonic motion. What is the largest possible amplitude the 5.00-kg mass can have for the...
  20. E

    Calculating Frequency of Oscillation for Different Masses on a Spring

    "A 0.25kg mass on a vertical spring oscillates with a frequency of 1.0 Hz. Suppose a 0.50kg mass were instead suspended from the same spring. What would be the frequency of oscillation in this case?" This is what I did: \frac{f_{1}}{f_{2}} = \frac...
  21. M

    Is the Motion of Particle P Simple Harmonic?

    A particle P of mass 0.2kg is attatched by an elastic spring of modulus 15N and natural length 1m to a point A of the smooth horizontal surface on which P rests. P receives an impulse of magnitude 0.5Ns in the direction AP. Show that while the string is taught, the motion of P is simple harmonic...
  22. K

    Simple Harmonic Motion and frequency of a spring

    I have one question here,I fail to understood what is Q of the system,is anybody has an ideal on this? An object of mass 2 kg hangs from spring of negligible mass. The spring is extended by 2.5 cm when the object is attached. The top end of the spring is oscillated up and down in SHM with...
  23. M

    Simple Harmonic Motion - Alevel M3

    This is probably a really easy question. But alas the answer has eluded me thus far. Anyway, here is the question:- Points O, A and B lie in that order on a straight line. A particle P is moving on the line with S.H.M period of 4s, amplitude 0.5m and centre O. OA is 0.1m and OB is 0.3m. When...
  24. S

    Simple harmonic motion and maximum speed

    I got a question, what is the maximum speed of an object undergoing SHM? and what is the max. acceleration. I am not sure how to solve this without any data given. I know that velocity v=-Awsinwt. and accleration is a=Awcoswt. So how am I to find the max speed and max acceleration?. Pls help.
  25. K

    Calculating Initial Velocity with Spring Constant and Mass: Homework Problems

    These questions on my homework are so hard. anyone get them? "The Spring constant for the spring in a special cannon is 1800N/m. In cocking the cannon, the spring is compressed .55m. What is the initial speed of a 7.0 kg cannonball at rest on the free end of the spring when it is released?"...
  26. E

    Solving Simple Harmonic Motion: Finding First Times for X=0 and V=0

    I am trying to solve the part c of the question. I know the initial condidtions of the motion which are Xo=3 and Vo=50 my W=10 , B1=3 B2=5 and my equation is x(t)=3cos(10t)+5sin(10t), the question is at which first times x=0 and x(2dot)=V=0, Now, when I plot the equation on excel, I...
  27. G

    Which Formula Determines Pendulum's Period in Accelerating Frame?

    let us consider a bob suspended by means of a thread from a fixed point (wrt ground and i m considering ground to be an inertial frame in this problem ) . What will be the time period of small oscillations of this pandulum as seen by a man accelerating with an acceleration a along the horizontal...
  28. N

    How Accurate Are These Calculations for Simple Harmonic Motion?

    A block of mass 0.5kg moving on a horizontal frictionless surface at 2.0 m/s collides with and sticks to a massless pan attached to the end of a horizontal ideal spring whose spring constan is 32 N/m. a) Determine the function for x(t), the displacement from equilibrium position as a function...
  29. N

    Physics - Simple Harmonic Motion

    A block of mass 0.5kg moving on a horizontal frictionless surface at 2.0 m/s collides with and sticks to a massless pan attached to the end of a horizontal ideal spring whose spring constan is 32 N/m. a) Determine the function for x(t), the displacement from equilibrium position as a function...
  30. D

    Simple harmonic motion summary

    What is mean by harmonics in SHM?
  31. A

    Calculating Maximum Speed of a Child on a Swing | Simple Harmonic Motion

    I don't find this topic too difficult but I am really stuggling on a question (im sure its really simple though) A child on a swing rises throught a height of 0.5m. Ignoring resistive energy losses, calculate the maximum speed of the child (the child doesn't increase/decrease swing height and...
  32. K

    Simple Harmonic Motion oscillations

    A 0.49 kg mass attached to a spring (k = 19.8 N m-1) is performing SHM on a smooth horizontal surface. Calculate the periodic time of these oscillations, in s. what equation links with T=2pi/w to give T or how do i use a=-ky/m. thanks in advance
  33. S

    Simple Harmonic Motion - seemingly easy yet

    The function x = (2.0 m) cos[(2pi rad/s)t + pi/2 rad] gives the simple harmonic motion of a body. Find the following values at t = 4.0 s. (a) the displacement: ____m Correct me if I am wrong, but to get x all I have to do is just plug 4.0 s in for t in that equation mentioned above right? I...
  34. N

    Simple Harmonic Motion acceleration problem

    This is a problem right out of the book. My professor worked it out in class but now that I look over it I'm not sure why he chose the method he did. This is the problem exactly as it is stated in the book: From this I was able to derive several other components that will be very helpful for...
  35. R

    Simple Harmonic Motion formula

    Hi. I've got a problem here about Simple Harmonic Motion. There is "formula" in our physics coursebook for the distance traveled by an object : s=4AN=4At/T s-distance travelled A-amplitude N-number of cycles t-time T-period Is it true for every case or just for N=1, 2 , 3 ? I guess...
  36. B

    Some one me with part B. (Simple Harmonic Motion)

    Some one please help me with part B. (Simple Harmonic Motion) Online waiting! Simple Harmonic Motion A block of mass M = 10 kg is hanging, at rest, from a spring with a force constant of 250 N/m. There is also a very small penny sitting on top of the block. (Note: The penny is not stuck to the...
  37. B

    Some one me with part B. (Simple Harmonic Motion)

    Simple Harmonic Motion A block of mass M = 10 kg is hanging, at rest, from a spring with a force constant of 250 N/m. There is also a very small penny sitting on top of the block. (Note: The penny is not stuck to the block and can leave the surface of the block.) The block is now pulled down...
  38. K

    What Amplitude Ensures a Computer Withstands 32g in Simple Harmonic Motion?

    A computer to be used in a satellite must be able to withstand accelerations of up to 32 times the acceleration due to gravity. In a test to see if it meets this specification, the computer is bolted to a frame that is vibrated back and forth in simple harmonic motion at a frequency of 11.4 Hz...
  39. I

    How Do You Solve These Simple Harmonic Motion Problems?

    1. three 10,000kg ore cars are held at rest on a 30degree incline on a mine railway using a cable that is parrallel to the incline. The cable is observed to strech 15cm just before the coupling between to lower two cards creaks, detaching the lowest car. Assuming the cable obeys Hook's Law...
  40. T

    Calculating Period for Simple Harmonic Motion in Physics Lab

    First, I hope this area is the right one for my question. I am working on a lab for Phyiscs I. The lab title is "Simple Harmonic Motion". Okay her is the deal and the question. My instructor told us to find the period by dividing the Time recorded by the number of oscillations (back and forth...
  41. I

    How can I find the value of phi in a simple harmonic motion equation?

    http://noether.physics.ubc.ca/physics153/assign72k5.pdf I don't get number 1 c, which equation do i use? and in general, how would I be able to find phi? OK, i figured i should find the first derivative of the displacement formula, which becomes v = -Asin(wt + phi) but that still undoable, how...
  42. C

    Simple Harmonic Motion assignment

    Hi, I'm having a few problems with an assignment. Here is the question, and the progress that I've made so far. (If you can call it progress... ) Q) A 500g cylinder of base area a=20cm^2 and height h=30cm is floating upright in water. A 50g mass resting on top of the cylinder is suddenly...
  43. D

    Show that the ball undergoes simple harmonic motion

    The problem goes as following: Solid ball (Solid sphere) of mass M and radius r is kept at the equilibrium position on a concave surface of radius R , for small displacement up the concave surface , show that the ball shows SHM motion assuming the ball rolls without slipping. I have been...
  44. E

    Simple Harmonic Motion and time equation

    Question: An object is undergoing simple harmonic motion with period 0.305 s and amplitude 6.05 cm. At t=0 the object is instantaneously at rest at x=6.05 cm. A. Calculate the time it takes the object to go from x=6.05 cm to x = -1.49 cm. I'm thinking \omega = \frac{2\pi}{T} = 20.6 rad/s. If...
  45. R

    How Do You Solve for C1 and C2 in Damped Simple Harmonic Motion?

    I'm having trouble with this problem. I want to get it into a form with cos but I'm stumped. The solution for damped simple harmonic motion is given by x = (e^(-rt/2m))(C_1*e^(iw't)+C_2*e^(-iwt)) If x = Acos phi at t = 0, find the values of C_1 and C_2 to show that x'=(approx)...
  46. E

    Finding the phase angle in simple harmonic motion

    Question: A frictionless block of mass 2.35 kg is attached to an ideal spring with force constant 310 N/m. At t=0 the spring is neither stretched nor compressed and the block is moving in the negative direction at a speed of 12.6 m/s. 1. Find the amplitude. I got this without a problem...
  47. C

    Question about simple harmonic motion

    A square block, with a mass of 3.40 kg and edge lengths d = 6.00 cm, is mounted on an axle through its center. A spring of spring constant k = 1190 N/m connects the block's upper corner with a rigid wall. Initially the spring is at its rest length. If the block is rotated by 3° and then...
  48. 1

    Solving Simple Harmonic Motion: Find Angular Freq & Amp.

    Question: A particle undergoing simple harmonic motion has a velocity v1 when the displacement is x1 and a velocity v2 when the displacement is x2. Find the angular frequency and the amplitutde of the motion in terms of the given quantities. The answers given in the back of the book are...
  49. D

    Simple Harmonic Motion and time period

    A particle follows SHM with its eqn.of motion being s(x,y)=Asinwt i + 3Asin3wt j What is its time period? Also find the expression for total mechanical energy wrt time. I tried it in the following way V=Awcoswt i + 3Awcos3wt j = Aw[(coswt)^2 +9(cos3wt)^2]^(1/2)...
  50. W

    2 problems on simple harmonic motion

    these are 2 qn on simple harmonic motion which i am not sure if my solution is right or not. 1) A thin rod, length L hinged at one end, connected to a spring at the other end. Take the spring constant to be K. What is the angular frequency? My solution: let the displacement from equil. to...
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