Simple harmonic motion Definition and 910 Threads

So when I attempted this question I was kind of stumped, as I have dealt only with SHMs in the same direction, which I can just add up. I know that this is possible because when we represent the SHMs as PHASORS, they rotate with some constant angular speed and can be treated as vectors. How do...

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Using the above equations and the given information, I get ##k=2.48*10^-4## 2.47∗10−4max=7.56∗10−5##Vmax=7.58*10^-5## and ##total energy=8*10^-6 joules##. My answer is clearly the wrong order of magnitude. The book answer key says 400 joules. My calculation for total energy was...

The force on the particle is $$F(x)=-V'(x)$$ By equating this to zero we find points of stable equilibrium. There are three such points $$x=0$$ $$x=a^3\left ( \frac{-3a^2\pm\sqrt{9a^4+16E_0}}{2E_0} \right )$$ Next we use a Taylor approximation to ##F##. $$F(x+\Delta x) \approx...

Here is a picture of the situation Let's model the wire as acting like a massless spring with spring constant ##k##. Let's define our coordinate system to be a ##y##-axis that has zero at the initial position of the wire (the landing position, and the equilibrium position of the spring). At...

Though I am interested in directly answering the question above, I am more interested initially in general calculations for this problem. Below I try to figure out what the normal force on the ball is based on the angle ##\theta##. The calculation seems incorrect and I would like to know where I...

I'm doing a personal experiment where I take a conical spring (that is, a spring with two different diameters on either end), hang it from the ceiling, and measure the period of oscillation for different masses hanging below the spring. I do this for two different orientations of the spring; one...

A spring attached to a mass undergoes simple harmonic motion. From Newton's second law we have ##ma=-qx## where ##q## is the spring constant. $$x''+\frac{q}{m}x=0$$ A second order equation with constant coefficients. The characteristic equation is ##r^2+\frac{q}{m}=0##. The roots are...

A horizontal metal plate connected to a vibration generator is oscillating vertically with simple harmonic motion of period 0.080 s and amplitude 1.2 mm. There are dry grains of sand on the plate. The frequency of the vibrating plate is kept constant and its amplitude is slowly increased from...

I put 0, but that is incorrect. Why is 0 an incorrect answer? This is confusing, as if the pendulum is in free fall, wouldn't there be no SHM at all?

All simple harmonic motion must satisfy $$\frac{d^2s}{dt^2}=-k^2s$$ for a positive value k. The most well known solution is the sinusoidal one $$ s=Acos/sin(\omega t + \delta)$$ A is amplitude, ##\omega##is related to frequency and ##\delta## is phase displacement. My lecturer said that there...

TL;DR Summary: Prove that a sum of trigonometric ratios is periodic but not not simple harmonic. We need to prove that ##x = sin{\omega t} + sin{2\omega t} + sin{4\omega t}## where ##x## is the displacement from the equilibrium position at time ##t##. I can see that each term is a SHM, but...

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.

I have successfully completed parts A, and B, however, I am confused on Part C. Here was my attempt and the answer key's attempt: My attempt: Since I correctly knew the speed after the collision, and the gravitational potential energy after the collision if I set h=0 at when it was at rest...

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...

A textbook I am using gives the basic eqn of motion of shm as follows : X = Asin(wt + €) V =Awcos(wt+€) But other textbooks and online sources are interchanging sin and cos in above equations, so which is the correct one? Or does it depend on the phase constant €?

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)?

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>

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...

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 ;)

I am only asking about the answer to part B, but reading through part A may give some some context/familiarity. Below is the answer to part B: I largely understand the graph except for 1 part. My understanding is as such: At first, ##x = \frac {\mu_k m g } {k}##. Force exerted by the...

Take rightwards as positive. There are 2 equations of motion, depending on whether ##\frac {dx} {dt} ## is positive or not. The 2 equations are: ##m\ddot x = -kx \pm \mu mg## My questions about this system: Is this SHM? Possible method to solve for equation of motion: - Solve the 2nd ODE...

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...

Summary:: I have come across a situation where I seem to get different equations of motion for an oscillating system. Please do help me find out where I went wrong. *I am not asking how to solve the problem* I am going to consider 4 parts of the cylinder's motion, as listed below. (There is...

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...

I understand the masses will accelerate toward each other with the same varying speed before they reach the natural length of the spring. Then they continue to approach each other while compress the spring, that'll slow their speeds down definitely. So my question is, how could we calculate how...

The other day when I solved a spring mass damper system in Matlab, I was curious how in olden days would have people solved the equation. We all know the 2nd order differential equation of the system: However if I know the time, damping coefficient, stiffness and mass, will I be able to find...

See the question : https://www.thestudentroom.co.uk/att...hmentid=978958 The mark scheme/answer : https://www.thestudentroom.co.uk/att...hmentid=978956 I have got the answer to the vertical height gained = 1.355 m. No problem. But not the value of the percentage difference. Their value : 23%...

How is the answer to 3 (d) is found?

I've just learned about simple harmonic motion and I've been given the following examples: The physical pendulum (for small oscillations sin(theta)~theta), with the formula (1st pic), and the LC circuit, with the formula (2nd pic). If possible, I need the demonstration for these 2 formulas...

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...

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...

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

I don't know how to start doing this homework. I would like help to orient myself.

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...

Im not sure how to find k if I'm not given a force or period.

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

Greetings, I'm happy to find such an enthusiastic community with an encyclopedic knowledge and mathematical rigor. I'm a Biomedical Engineering Researcher that's had to breach into the world of condensed matter physics to better understand the physical principles of the piezoelectric crystal...

c = Critically Damped factor c = 2√(km) c = 2 × √(150 × .58) = 18.65 Friction force = -cv Velocity v = disp/time = .05/3.5 Friction force = - 18.65 * .05/3.5 = -.27 N I am not sure if above is correct. Please check and let me know how to do it.

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...

I found the amplitude of the simple harmonic motion that results (0.367, and I know this is correct because I entered it and it was marked as a correct answer), and assumed it would be the same value for the maximum compression since x(t) = Acos(wt). And, since the maximum value of cosine is 1...

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...

In the given problem, i can understand that after placing the two blocks in equilibrium it oscillates with an amplitude of The answer for (b) is given as To my knowledge, m2 separate from m1 when the acceleration is greater than gsinø and so they should be separating only at max displacement...

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.

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...

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...

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 ##...

Continuing on from the summary, the chapter has given a graphed example. We are shown a regular cosine wave with phase angle 0 and another with phase angle (-Pi/4) in order to illustrate that the second curve is shifted rightward to the regular cosine curve because of the negative value. Now, my...

Hi. I'm trying to determine the frequency of an block (roughly a rectangular prism) when the oscillation is due to a shear restoring force. Here is a diagram: In the derivation, ##\rho## is the density of the block,##G## is the shear modulus of the block, ##y## is the elevation of the element...

The question asks for a bunch of stuff, but I have everything except part d down. a) Setting the mass of lemons as m1, I used m1*gh = 1/2mv^2, solving for v of the lemons as v = √2gh, where h is the height at which it is dropped. Then, I used COM and had this equation (not 100% sure if right)...