Harmonic motion Definition and 1000 Threads

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) ...

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...

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...

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...

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...

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...

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...

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...

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

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?

Homework Statement A block on a horizontal surface is attached to two springs whose other ends are fixed to walls. A light string attached to one side of the block initially lies straight across the surface. The other end of the string is free to move. There is significant friction between...

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

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...

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...

Hello I was given this problem, and I have two possible answers and I really just need someone to verify which one is right, or at least in the right direction. Thanks! Homework Statement A cart is floating on an airtrack and is connected by a spring to one fixed object. The cart executes...

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)...

Hey PF, my book either got sloppy in a derivation or I am not connecting two very obvious dots. It gives the energy of the damped harmonic oscillator as E = (1/2)mv^2 + (1/2)kx^2 then takes the derivative with respect to time to get dE/dt. then it gives the differential equation of motion...

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)...

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...

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...

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...

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...

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...

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...

Homework Statement A mass of 0.4 kg, hanging from a spring (k= 80N/m) is set into an up-and-down SHM. What is the speed of the mass when moving through the equilibrium point? The starting displacement, A, is 0.10 m. Homework Equations a = -kx/m ω = 2pi/TThe Attempt at a Solution I tried to...

Homework Statement The function x = (7.4 m) cos[(5πrad/s)t + π/5 rad] gives the simple harmonic motion of a body. At t = 6.2 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion...

Problem: Show that the combined spring energy and gravitational energy for a mass m hanging from a light spring of force constant k can be expressed as 1/2 ky2, where y is the distance above or below the equilibrium position. Figure shows a block connected to spring, where equilibrium is...

Homework Statement I was wanting to get some clarification on some of the simple harmonic motion equations. So, say for example there is a box of mass "m" undergoing simple harmonic motion attached to a spring of spring constant K on a horizontal surface. To find where the box is, as a...

Homework Statement a small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is the same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such that the small mass is at the top. Find the least R/r ratio such that the...

The nonlinear oscillator $y'' + f(y)=0$ is equivalent to the Simple harmonic motion: $y'= -z $, $z'= f(y)$ the modified Symplectic Euler equation are $$y'=-z+\frac {1}{2} hf(y)$$ $$y'=f(y)+\frac {1}{2} hf_y z$$ and deduce that the coresponding approximate solution lie on the family of curves...

Homework Statement An object moving with harmonic motion has an acceleration of -2 m/s^2 when the elongation is 0.5 m. Determine the angular frequency and the velocity and acceleration for t=1s. Homework Equations a=-ω2x (1) x=Acos(ωt+θ) (2) a=-Aω2cos(ωt+θ) (3) The Attempt at a...

Hi I am using Simple Harmonic Motion in a Matlab/Simulink model. Instead of using a motion for a simple pendulum, I decided to use a spring with a mass. The reasons for this is because my example is more like a lever attached to a pivot point and having an object at the end with a mass. A...

Homework Statement A particle moves along the x axis. It is moving initially at the position 0.280 m, moving with velocity 0.200 m/s and acceleration -0.450 m/s^2. Suppose it moves with constant acceleration for 4.10 s. (a) Find the position of the particle after this time...

Homework Statement Hi, so my question is about a damped simple harmonic motion experiment The experiment is as follows: A 30 cm ruler with a needle attached to it is clamped to a bulldog clamp. The needle is placed in a beaker of water so that it is just inside the water ( by about...

The problem is a ball is dropped onto a spring and the spring compresses .95m. The ball then sticks to the spring and oscillates with a period of 1.1 seconds and has a mass of 6kg. I thought that the equation mg(h+x)=1/2(k)(x^2) would be what i would use. I got h=.47m I also...

Homework Statement Write a simple harmonic motion with amplitude 14cm , frequency 3.0Hz , and maximum displacement at t=0.The Attempt at a Solutiony (t) = A cos (ωt) = 14 cos (2πt/T) Dealing with angular frequency is easy. But deal with natural frequency throws me off course.

1. What is the difference between ψ = Amod(t) cos (wavt)and the simple harmonic oscillator? 3. A. The amplitude is time dependent B. The amplitude,Amod , is twice the amplitude of the simple harmonic oscillator, A. C. The oscillatory behavior is a function of ? instead of the period, T...

Homework Statement An object is undergoing simple harmonic motion with frequency f = 3.1 Hz and an amplitude of 0.15 m. At t = 0.00 s the object is at x = 0.00 m. How long does it take the object to go from x = 0.00 m to x = 7.00×10-2 m. Homework Equations x(t)=Asin(ωt) The Attempt...

I was hoping that someone could explain why these different equations can be found from different sources please. The time dependent position, x(t), of an underdamped harmonic oscillator is given by: x(t)=e^{-\gamma t}acos(\omega_{1}t-\alpha) where \gamma is the damping coefficient, and...

Homework Statement Determine the motion of this mechanical system satisfying the initial conditions :- y1(0) = 1 y2(0) = 2 y1'(0) = -2*sqrt(6) y2'(0) = sqrt(6) Hint : there are 4 different methods you can use to solve this problem. They all give the same exact result. I need to...

If we apply the small angle approximation so that a simple pendulum can be considered to be under going SHM, what kind of potential energy would the pendulum bob be having? If the answer is gravitational potential energy, then we have a contradiction because this would mean that the bob would...

For a mass on a spring (vertical set up) why is potential energy U defined as 1/2 kx^2? This is just the elastic potential energy. Shouldn't it be U = 1/2 kx^2 + mgh? Both the elastic AND potential energy? Also, for a simple pendulum at a very low amplitude, the potential energy is all...

For a mass on a spring (vertical set up) undergoing SHM, we equate the restoring force, -kx, to -ω^2 x, coming to a conclusion that ω = \sqrt{\frac{k}{m}}. My question is, is the restoring force |mg - T| Where T is the tension in the spring? Because this seems to be the net force. I am used to...

Simple harmonic motion (Again) :( This is not a question about a problem it is more about the position of a simple harmonic oscillator as a function of time:) I went through it in a lecture yesterday and found using the energy in simple harmonic motion to bex(t)= A cos(ωt +φ) Which is fine...

I have a question about the derivation that I have attached! I understand that both KE and U are 1/2 kA^2 So how is it that the two combine is also equal to 1/2kA^2Not sure if I'm missing something but I'm a little confused :(

Homework Statement This is a required analysis for my Physics II lab. We recorded the motion of an object oscillating on spring, and are asked to use the slopes of different graphs that we plotted using the data collected in lab in order to find the spring constant (k). Both graphs were...

Homework Statement Find the period of low-amplitude vertical vibrations of the system shown. The mass of the block is m. The pulley hangs from the ceiling on a spring with a force constant k. The block hangs from an ideal string...

What is a good way to memorize that ## \omega = \sqrt{\dfrac{k}{m}} ## ? I always confuse it with: ## T = 2\pi \sqrt{\dfrac{m}{k}}## , and can never tell them apart. (i guess part of it is that I'm not too familiar with it yet)

Homework Statement A 1.15-kg mass oscillates according to the equation x = .650cos(8.40t) where x is in meters and t in seconds. Determine a)the amplitude, b)the frequency, c) the total energy of the system, and d) the kinetic and potential energy when x = 0.360m. Homework Equations x...