# 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. ### Solve First Year Harmonic Motion Problem: Cylinder Rolling

Thank you guys for taking the time to read this - I'm decently struggling with first year and need some tips on how to properly conceptualize problems and learn what the right approach is on certain problems. Have a wonderful day, again thank you for checking this post out!
2. ### Solving for Simple Harmonic Motion: A Picture Problem

Here is a picture of the problem It is not clear to me how to really prove that the equation for ##\theta(t)## is simple harmonic motion, and what the period of this motion is.
3. ### Bungee jump | simple harmonic motion

As you all know, a bungee jump is where a person is tied to a cord and the person jumps off and bounces up again. The natural length of a cord is 75 metres. Then when a person is attached onto the cord, the length becomes 83 metres when the person is at rest. I am sure that the person is not...
4. ### Study of harmonic motion of a liquid in a V shaped tube

A V-shaped tube with a cross-section A contains a perfect liquid with mass density and length L plus and the angles between the horizontal plane and the tube arms as shown in the attached figure. We displace the liquid from its equilibrium position with a distance and without any initial...
5. ### I The speed of a waves on a string in Simple harmonic motion

The speed of a wave in simple harmonic motion on a string is $$v= \sqrt{\frac{F}{\mu}}$$ where v= the horizontal velocity of the wave on a string. Is the F the horizontal force or the resultant force (combination of Fy and Fx)?
6. ### B Is simple harmonic motion also a pure translatory motion?

Is simple harmonic motion also a pure translatory motion?"A rigid body moves in pure translation if each particle of the body undergoes the same displacement as every other particle in any given time interval" [Halliday and Resnick, Physics].If not,then how does shm deviate from this definition>
7. ### Inclined plane with pulley and spring

1) By the Work-Energy Theorem, ##W=K_f-K_i=\frac{1}{2}I_{0}\omega^2=\frac{L^2}{2I_0}.## 2) By assuming that the initial length of the spring is ##0##, calling its final length ##S## and ##T## the tension in the rope connecting the pulley and mass ##m_p## I have: ##\begin{cases}(kS-T)r=0\\ m_p...
8. ### An object oscillating in simple harmonic motion

Since it passes through the origin every ##3.6s## the period is ##T=3.6s## hence ##\omega=\frac{2\pi}{\omega}=\frac{2\pi}{3.6}\frac{rad}{s}## thus ##A=\frac{v_{max}}{\omega}=\frac{1.2}{\frac{2\pi}{3.6}}m\simeq 0.69m## and ##a_{max}=\omega^2 A=(\frac{2\pi}{T})^2 A=(\frac{2\pi}{3.6})^2 \cdot...
9. ### Damped harmonic motion problem

Hi ! Problem : y = 5 e^-0.25t sin (0.5.t) (m, s). Determine the deviation at a time when the amplitude has dropped to 1/5 of the original value. I tried with A=A0 e^-bt=5 e^-0.25t - Do i need to determine the time here or recreate the deviation equation when A decreased ? I don't understand...
10. ### Superposition of two simple harmonic motion

Hey! I am stuck in this problem, i don't know how to sum this ecuations. I remember that its possible because the direction is the same So, i try to sum like this: cos (t+5325) + 1.5 cos (t+5325) =1.5 cos (t+5325) I don't know if i fine. I thanks your help, please ;)
11. ### Simple harmonic motion (help please)

The first ecuation values i am 99% that is correct. But, in the second and three problem i don't know if my results are ok. The problem number 2 i comprobate with the teacher that te aceleration its correct, so, with this i calculate the velocity. I use like example the second problem for try...

13. ### Harmonic motion - Find the Mass held between two Springs

So first I find the energy using the eqn (1/2)kA^2. Since there are two springs with the same k I multiply it by two to get kA^2. Energy I get is 2.0475, Now I use E=(1/2)m(wA)^2 to find mass. Again since there are two springs I use E=m(wA)^2. m=E/(wA)^2. w=(2(pi))/T btw. I get the answer of...

15. ### Harmonic motion and waves

Solutions in a file.
16. ### Simple Harmonic Motion of a Mass Hanging from a Vertical Spring

Assuming zero spring mass and zero friction, At the greatest value of x, the loss in gravitational potential energy should equal the loss in elastic potential energy. so I did (1/2)kx^2=mgx to isolate x in the formula, x=(2mg)/k then I plugged in my values so: (2*13.6*9.81)/8.8= 30.3218...
17. ### Oscillation of a particle on a parabolic surface [equation of motion]

Hi, I have a particle on a parabolic surface $$y = Ax^2$$ and I have to show that the frequency is $$\omega = \sqrt{2Ag}$$ I don't know how to deal with a parabola. I don't think I can use the polar coordinates like a circle. I don't see how to start this problem and in which coordinates...
18. ### Harmonic Motion Problem - Finding oscillation of charges in a circuit

So since V(cap) + V(ind)=0 then Q/C + L dI/dt=0 Now since I=dQ/dt, I can replace dI/dt with d^2Q/dt^2 resulting in Q/C + L d^2Q/dt^2 =0 Now L d^2Q/dt^2 looks like a harmonic motion thing I can solve, where w^2=L. This means I can find w. I get 0.0005385. Now my issue is using this w gives the...
19. ### Harmonic Motion of a Mass between two springs

So first I found the total energy of the system by calculating the potential Energy, Ep=0.5k(l^2+l^2) and get 2.0475 (this part is right). Then I find w using the period T=2pi/w, so w=2pi/1.21=5.1927 I also found the amplitude using E=1/2kA^2, so A=sqrt(2E/k)=0.212132 Now this is the part I...
20. ### Simple harmonic motion problem

How is the answer to 3 (d) is found?
21. ### Simple and driven harmonic motion

I know you can't solve it and just give it to me, I just want to know what I'm supposed to do, if you need any more information or clarification please let me know. Thank you for taking the time to help me!
22. ### Simple Harmonic Motion Question

First I use young's modulus to solve for delta y. I get 5.67x10 -5. I am not sure what to do after this, but this is my attempt. Next I do T = 2delta y sqrt(m/k) (I am not sure if I am supposed to put 2 delta y) Solving for f, i get f = 1/(2delta y sqrt(m/k)) F = kx, mg = kx, m = kx/g...
23. ### Energy loss in simple harmonic motion causes the time period to shorten?

https://www.asi.edu.au/wp-content/uploads/2016/10/ASOEsolns2012.pdf Q11 D) Markers comments: Few students reached part (d) and very few of those who did realized that the amplitude does affect the time taken for each of Mordred’s bounces. i.e. the energy losses results in shorter periods...
24. ### Classical Book for simple harmonic motion

sites or books for SHM high school and undergrad level. i want to understand SHM from the ground up and I am finding difficulty with my current sources
25. ### Simple harmonic motion homework

I don't know how to start doing this homework. I would like help to orient myself.
26. ### Calculating Period of System with Masses, R & dX

Here is the picture on the system. I have to find the period (T). The masses, R and dX is given. The systam at first is at rest, then at t = 0 we pull the plank to dX distance from its originial position. In the thread...
27. ### Simple harmonic motion equations as a function of time

I conducted a mass-sprig experiment to see how stiffness of a spring and mass affect the frequency of oscillation. In addition to this to this i have to plot a graph to show displacement,velocity and acceleration of the mass as a function of time.From my research online For the displacement as...
28. ### The periodic time of an elastic string's oscillation

i guess he is asking for the periodic time : $$Tension = \frac {λ*y}{a}$$ $$\lambda= mg$$ $$y =3a$$ $$T = 3mg$$ $$F = T-mg\Longrightarrow F = 3mg-mg = 2mg$$ $$m{y}''=2mg$$ $$y'' = 2g \therefore\frac { dy'}{dt} = 2g \Longrightarrow y' = 2gt+c1$$ by applying the boundary conditions and...
29. ### Simple Harmonic motion calculation for a mass on a spring

Im not sure how to find k if I'm not given a force or period.
30. ### Zero Amplitude Damped Simple Harmonic Motion with k=0.7s^-1 and f=3Hz

Hi guys sorry if this is the wrong thread, I have a damped simple harmonic motion pictured below, i have to find the inerval t=0 and t=1 for which the amplitude of x(t) is considered to be zero. The behaviour of the graph below can be described as e^-kt cos(2πft) k=0.7s^-1 and f= 3Hz
31. ### How to know whether motion is simple harmonic motion or not?

I am reading "Coulomb and the evolution of physics and engineering in eighteenth-century France". There it is said in page 152 para 1 that "Coulomb found that within a very wide range, the torsion device oscillated in SHM". My questions are: (1) By just looking at the time period of the...
32. ### Simple Harmonic Motion Amplitude

Using A = x0, B = v0/ω I get ω = 4π, A = 1, B = 1/4π then converting to phase/magnitude form \sqrt{A^{2} + B^{^{2}}} = \alpha \sqrt{1^{2} + \left ( \frac{1}{4\pi }\right )^{^{2}}} = \alpha = \frac{1}{4\pi }\sqrt{16\pi^{2} +1} However the answer in the back of the book has α = 1 Is...
33. ### Harmonic motion of four meter sticks

inertia of center = [(1/12) m*L^2 + m(L/2)^2]*4 inertia of center = (4m*L^2)/ 3 inertia around pin = (4m*L^2)/ 3 + 4m(L/ 2^(1/2) )^2 inertia around pin = (10m*L^2)/ 3 inertia around pin = (10*0.1*1^2)/ 3 = 0.33 kg*m^2 d= 1/2^(1/2) = 0.707m (m*g*d/inertia)^1/2 = 2pi/period...
34. ### Initial conditions in simple harmonic motion

I have the formula for amplitude ##A=\sqrt (x_0^2 + \frac{\dot x_0 ^2}{\omega^2})##. But ##x_0## and ##\dot x_0## refers to the initial conditions, and the information that I'm given is not related to the initial conditions, or at least I'm not told so.
35. ### Finding equations for simple harmonic motion given a graph

Well, this is a problem which makes you think more about concepts than numbers, so I want to see if I've done it correctly. 1) I draw a simple pendulum in an elevator, where you have weight, tension and a pseudo-force. In this situation the effective gravity may be changing due to different...
36. ### Prove that a mass has simple harmonic motion

If I write Newton's equations, seen inside the room and with non tilted axis we have: ##x) N.sin(\alpha)-Fe.cos(\alpha)=m.a_x## ##y) N.cos(\alpha)+Fe.sin(\alpha)-m.g-f*=m.a_y## Where ##f*=ma##, ##Fe## is the elastic force. Then, how can I realize about simple harmonic motion? I also can think...
37. ### Simple harmonic motion -- manipulating SHM equations

My workings: ##D(t) = Asin\omega t## ##v(t) = \frac{\text{dD}}{\text{dt}}=Acos(\omega t)\omega## ##v(t) =Acos(\omega t)\omega## When displacement half of amplitude, ## Asin\omega t## = 0.5##A## ## sin\omega t## = 0.5 ##v(t) =Acos(\omega t)\omega## ##v(t) =\omega (0.5Asin\omega t)cos \omega t ##...
38. ### How to find the velocity of a wave in simple harmonic motion given time

The graph provided is below. The problem asks for the speed of the wave at 0.12s. I used the formula v=w*xmax*cos(wt), provided in our textbook where xmax is the amplitude of 2 cm, w (omega) is 2pi divided by the period of 0.2. However, for some reason this formula doesn't give me the correct...
39. ### Simple Harmonic Motion Experiment Problem

I think you could try to solve for the forces based on when the spring falls from an incline at various angles theta, but I am not sure. Or spring potential energy? I'm really confused. Is there any other method? Could it involve using water and wave harmonics? (We learned waves and sound...
40. ### Simple Harmonic motion of a Pendulum

First, I decided to solve for the coefficient in front of the cosine simple harmonic function for velocity. I know there is max velocity of 30cm/s at time = 0 , so I plug it into velocity function. xmax * w = A v(t) = Acos(wt) 0.3 = Acos(w*0) A = 0.3 Then I have my velocity function...
41. ### Is this Simple Harmonic Motion?

I've been going to the theme park almost every year-and this year in my Physics class we are learning mechanics, more specifically Simple Harmonic Motion. My teacher told us that for an object to have 'Simple Harmonic Motion' it must have oscillatory motion (like a pendulum going back and...
42. ### Simple harmonic motion of a bar pivoted at one end

Hi, I am unsure how to proceed with this problem. I believe that I can correctly calculate the frequency of the oscillations for a bar that is not suspended from a spring but I do not know how to take the effect of the spring into account. The answer given by my professor is ...
43. ### High school Physics - Simple Harmonic Motion

I started off by finding when Fg=Fx: (72)(x)=(31)(9.8) x=4.2193m After this I'm stuck and have a few things I'm confused about: When the penguin's jumping, is there elastic energy? (because the rope's getting compressed? Or maybe not). Also, I know you can use energy conservation, but...
44. ### Simple harmonic motion interpretation problem

I'm in trouble trying to understand the expression ##t= \frac{1}{\omega} cos^{-1}(x/A)## that comes from ##x = Acos(\omega t)##, in which ##A## is the amplitude, ##t## is time and ##x## is displacement. When ##x = 0##, ##t = \frac{\pi}{2\omega} ##, shouldn't it be 0 since there was no movement?
45. ### Simple harmonic motion equation

Homework Statement Calculate the harmonic motion equation for the following case A=0.1m, t=0s x=0.05m, v(t=0)>0 a(t=0)= -0.8m/s^2 Homework Equations x(t)= +/-Acos/sin ( (2pi/T)/*t) The Attempt at a Solution [/B] A is given to be 0.1 so I simply place it into the equation. Now I have to...
46. ### Confused about a simple harmonic motion problem....

Homework Statement A vertical block-spring system on Earth has a period of 6.0 s. What is the period of this same system on the moon where the acceleration due to gravity is roughly 1/6 that of earth? Homework Equations w = √(k/m) w = (2Pi)/T T = 2Pi*√(m/k)[/B] The Attempt at a Solution So...
47. ### Position vs Time Graph: Simple Harmonic Motion

Homework Statement [see attached photo] I seek specific help with (a) only. The answers to this question are provided in the back of the textbook, so I know the answers (I hope). Homework Equations ##x(t)=Acos(\omega t+\phi _{0}),## ##v_{x}(t)=-A\omega sin(\omega t+\phi...
48. ### Simple Harmonic Motion derivation

Homework Statement Hookes Law gives: F = -kx. This is SHM. But I cannot see how to get to the sinusoidal expression from this. (In all the explanations, they cheat, and just introduce de novo Omega or Omega^2.) But how do you get to m. d2x/dt^2 = -x.(omega) ^2 Homework Equations F = -kx. m...
49. ### How to derive a formula for simple harmonic motion?

Homework Statement You need to derive a formula for undamped pendulum simple harmonic motion; 1. Starting from the middle point 2. Starting from the extreme point Homework Equations The solutions are; 1. s = s0 sin(2 pi f t) 2. s = s0 cos(2 pi f t) The Attempt at a Solution I can derive the...
50. ### Phase angle and Phase in Simple harmonic motion

I'm a teacher at a Senior High School in Indonesia. I have two Senior High School physics books (Indonesian book) written about simple harmonic motion formula: y = A sin θ = A sin (ωt + θ0) = A sin 2πφ = A sin 2π (t/T + θ0/2π) phase angle = θ = ωt + θ0 phase of wave = φ = t/T + θ0/2π But I...