Harmonic motion Definition and 1000 Threads

This is not really a homework problem but rather a question about an equation for displacement in damped harmonic oscillations that I've come across during revision for midterms. In my notes and in various textbooks the equation is given as x=C\mathrm{exp}(-\frac{b}{2m}t)\cdot\mathrm{exp}(\pm...

Period does not depend on amplitude. Correct? I deduced this from the equations for simple harmonic motion: ω=2πf ω=√(k/m)

Their equations are identical. Is there any difference between the two?

x(t)=Acos(ωt+ϕ)\\v(t)=-ωAsin(ωt+ϕ) I think my physics professor said in one of the lectures that: after setting up your position function by finding amplitude, angular speed, and solving for ϕ by setting t=0 and using the x(0) value given in the question, you need to to set t=0 in the velocity...

Homework Statement A mass is attached to a spring with a force constant of 32N/m. The spring and the mass are set into simple harmonic motion on a frictionless, horizontal surface. The period of vibration of this mass is 0.4 seconds. a) Calculate the object's mass b) Calculate...

All Questions are shown on pictures. My Calculated answers: A1(a) R= 19.21∠68.7o N (b) E = 19.21∠-111.34o N or = -19.21∠68.7o N <--- Is't either one answer is correct or not? If not, which answer is correct and why? Thanks. A2(b) I = 0.5mr2 = 1.125kgm2 A2(a) k=(I/m)1/2 = 0.212m...

Hi friends the problem is - https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/s480x480/155412_2656530589803_1383873256_n.jpg Attempt - As per the problem states, When the compound system will oscillate in its natural frequency, The frequency of the oscillation will be, √[k/(m...

Hi friends the problem is - https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/s480x480/60061_2656517749482_1458399262_n.jpg Attempt - As per the problem states, The net force on the particle will be ...

Hi friends the problem is - https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-snc6/s480x480/6405_2656465868185_1414230035_n.jpg Attempt - As per the problem states, For the first second equation of SHM, (using x = A sin ωt) a = A sin ω From here I get, sin ω = a/ A...

Homework Statement The two linear simple harmonic motions of equal amplitudes , and angular frequencies ω and 2ω are imposed on a particle along the axes of X and Y respectively. If the initial phase difference between them is π/2 , then find the resultant path followed by the particle...

Homework Statement This is a 3 part problem and I've successfully solved the first 2 parts, but I don't know what I did wrong in the third part. 1) mass of 346 g on a spring with constant 26.8 N/m on a horizontal + frictionless surface. Amplitude is 6.7 cm. In part 1 i found the total...

Homework Statement I'm doing a lab, and they want me to show the dependence of the period on different variables (displacement, mass, and length of pendulum). They ask me to "Fit curves to your plots to show the dependence. Use the curve fits from your plots to devise an equation for...

Homework Statement A machine part is undergoing SHM with a frequency of of 5hz and amplitude of 1.80cm. How long does it take the part to go from x = 0 to -1.80cm? Homework Equations x = Acoswt The Attempt at a Solution X is given and convert it to metres 0.018. I need to...

Homework Statement A 93-kg box hangs from the ceiling of a room—suspended from a spring with a force constant of 540 N/m. The unstressed length of the spring is 0.505 m. (a) Find the equilibrium position of the box. (b) An identical spring is stretched and attached to the ceiling and the box...

Homework Equations I do not why the particle does the simple harmonic motion. And how to find such innitial condition to satify r decreases continually in time. [b]3. The Attempt at a Solution [/b Is it need to take derivative of r?

Homework Statement I have a question pertaining to the simple harmonic motion of the midpoint of a guitar string with a frequency of 4.40 x 10^2 Hz and an amplitude of 1.60 mm. I've been asked to deduce the initial displacement, velocity and acceleration of the midpoint of the string, but am a...

I had a lecture regarding harmonic motion. he also derived equation related to pendulum motion with extended object and equation is following.(motion is a simple harmonic motion) d^2θ/dt^2+(RcmMg)θ/I=0 θ(t) = θcos(Ωt)+(ω/Ω)sin(Ωt) where Ω is defined angular frequency oscillation for all...

I'm trying to work out the differential equation for simple harmonic motion without damping, x''+\frac{k}{m}x = 0 I can solve it to x = c_1cos(\sqrt{\frac{k}{m}}) + c_2sin(\sqrt{\frac{k}{m}}) But the generalized solution is x = Acos(\omega*t + \delta) where A = \sqrt{c_1^2 + c_2^2}...

So, simple harmonic motion without damping is described generally by x(t) = Acos(\omega*t +\delta) Which is derived from the differential equation x''+\frac{k}{m}x = 0 We know that A = \sqrt{c_1^2+c_2^2} and tan\delta = \frac{c_1}{c_2} With the differential equation, dealing...

Homework Statement particle experiencing SHM with frequency f= 10 hz find the displacement x at any time t for the following initial conditions. @ t=0 x=0.25m v=0.1 m/sHomework Equations x=Asin(ωt+∅) v=Aωcos(ωt+∅)The Attempt at a Solution So with frequency I find ω which then is subbed into...

I was reading a book on wave and found that when they derive the equation of shm from the equation force varies with negetive displacement , they had taken a propotionality constant to make the force and displacement equal and they had taken frequency of the shm as the constant . So my question...

Consider a light flexible rod placed on a horizontle table with part of the rod (length say "x") hanging freely (ie without support of the table) see attachment for clarity A mass is also hung from the rod t one end. Are there any equations that relate the Period T of the end of the rod to...

Homework Statement Two springs each have spring constant k and equilibrium length (L). They are both stretched a distance (L) and attached to a mass m and two walls. At a given instant, the right spring constant is somehow magically changed to 3k (the relaxed length remains L). what is the...

So my friend and I were going through problems and this came up... Consider 3 straight, infinitely long, equally spaced wires (with zero radius, separated each by a distance d), each carrying a current I in the same direction. blah blah blah... part c) asks us... If the middle...

I know that simple harmonic motion is a type of periodic motion where the restorative force is directly proportional to the displacement so that the time evolution is sinusoidal but is there such a thing as just harmonic motion? 0r is harmonic motion just short for simple harmonic motion?

Homework Statement A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest: a.) find the force between the bottom of the box and the block as a function of time...

Homework Statement A block rides on a piston that is moving vertically with simple harmonic motion. (a) If the SHM has period 2.65 s, at what amplitude of motion will the block and piston separate? Homework Equations x(t)=xmcos(ωt + ∅) a(t)=-w2xmcos(ωt + ∅) Where xm is the amplitude...

A bucket of mass 2.0 kg containing 10 kg of water is hanged on a vertical ideal spring with constant 125 N/m, oscillating up and down with an amplitude equal to 3.0 cm. Suddenly arises a leaky in the bottom of the bucket so that the water flows at constant rate of 2.0 grams/s. When the bucket...

Homework Statement A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest: a.) find the force between the bottom of the box and the block as a function of time...

Homework Statement Two blocks mass m1 and m2 (m1 greater than m2) are joined by a spring (which can extend and compress) and both rest on a horizontal frictionless table. the blocks are pulled apart, held at rest and then released. describe and explain as fully as you can the sibsequent...

Homework Statement A metal sphere of mass 0.20kg is hung from a helical spring whose top end is clamped. the sphere is displaced by 0.030m below its equilibrium position, and then released. 20 cycles of oscillation, of amplitude 0.030m, occur in a time of 12.0s. calculate; (I) the spring...

I have to solve the following D.E. which describes how the amplitude of oscillation r, changes with time. r=f(t) \frac{dr^{2}cos^{2}t}{dt}=rsint How do I find r?

The question is: A 56.0 kg bungy-jumper hangs suspended from her bungy-cord, at rest. She is displaced from this position by 15.0 m downward, and then released. She bounces up and down, with a period of 5.800 s. Assume the woman undergoes simple harmonic motion, described by y(t) = X cos(2...

Homework Statement The motion of a particle is given by: x = (6.0m) cos(0.586t + 0.72) a) Find the amplitude b) Find the Period c) Find the first time for t>0 when v=0 d) Find the maximum acceleration e) Fine the phase at time t=1.38s Homework Equations x = A cos ωt T =...

Homework Statement A particle moving in simple harmonic motion with a period T = 1.5 s passes through the equilibrium point at time t0 = 0 with a velocity of 1.00 m/s to the right. A time t later, the particle is observed to move to the left with a velocity of 0.50 m/s. (Note the change in...

Homework Statement A spring is hung vertically from a support. A mass of 4.5 kg is hung from the lower end of the spring and is slowly lowered a distance of 22.0 cm until equilibrium is reached. This mass is then lowered to a point 15.0 cm below the equilibrium point and is then released...

Homework Statement A 250 gram mass is connected to a spring and executes simple harmonic motion. The period of motion is 0.5 seconds and the total mechanical energy is 0.50J. What is the amplitude of motion? Homework Equations ΔU = 1/2kx2 The Attempt at a Solution I get 1/2kx2 =...

I've been set this question by my tutor and I'm having difficulty doing it. A mass of 2 kg is hung from the lower end of a vertical spring and extends it by 40 cm. The mass is now pulled down a further 20 cm and is then released from rest so that it oscillates about the equilibrium position...

Homework Statement If the phase angle for a block-spring system in SHM is π/5 rad and the block's position is given x = xm cos(ωt + phi), what is the ratio of the kinetic energy to the potential energy at time t = 0? Homework Equations PE = (1/2)*k*[(max amplitude)^2]*cos^2(ωt + phi)...

Hi there, SalsaOnMyTaco here again. Homework Statement A 44 gram mass is attached to a massless spring and allowed to oscillate around an equilibrium according to: y(t) = 1.2*sin( 3.1415*t ) where y is measured in meters and t in seconds -What is the spring constant in N/m ? HELP...

Homework Statement I have trouble determining the system of forces in systems with strings like the following: Homework Equations The Attempt at a Solution My guess is it is: x1=L/3 x2=2L/3 mass 1: -kx1+k(x2-x1)=m1a1 mass 2: -k(x2-x1)+kx1=m2a2 I'm not sure...

(a) A box of mass m, attached to a spring, oscillates in simple harmonic motion on a frictionless surface as indicated in the figure below. Each time the box reaches the point of maximum displacement a child allows some sand to fall vertically into the box. This will gradually increase the mass...

Homework Statement Find a particular solution to the differential equation using undetermined coefficients. x^{''}+5x^{'}+4x=2sin2t x(0)=1 x'(0)=0 I know that the equation is underdamped because c<W_{0}, and that W_{0}=2. I know that the particular solution is...

Homework Statement A mass is oscillating on a spring with simple harmonic motion. Its amplitude is 0.80m and its maximum speed is 1.5m/s, at the point of equilibrium. What is the speed of the mass at 0.60m? Is there enough information to answer this question? The answer given is 0.75m/s...

A body moving with simple harmonic motion has an amplitude of 1 meter and the time for one complete oscillation is 2 seconds . Determine the velocity and acceleration of the body after 0.4 second from the mean position ? this is the answer : Vx = w root(r^2-x^2) ax=w^2.X w= 2Pi/t =...

Homework Statement Natural length is "l" and when a "m" mass is hanged on the P edge, it dragged by another "L" length. Point "O" is "4L" far from the floor. 1. Find \lambda 2. The mass will be hold at point "O" and released with the starting velocity √(gL). Find the velocity of the mass after...

Hi guys! I'd really like help with this as I'm stuck. Homework Statement Investigate the mathmatical relationship between period of a spring and mass. Finding the spring constant (k) from measuring periods with a spring and different hanging masses. Homework Equations T = 2pi...

Homework Statement A particle moves with SHM in a straight line. In the first second after starting from rest,it travels a distance of 1m in a constant direction. In the next second, it travels a distance of 2m in the same direction. Find its maximum acceleration Homework Equations...

Homework Statement http://img534.imageshack.us/img534/6503/questiono.jpg Homework Equations The Attempt at a Solution (a) I'm not sure how to approach this part. I appreciate any help to get me started. (b) I know that the period of oscillation is given by T'=\frac{2 \pi}{\omega '} I...

Homework Statement A car with mass 1220kg including the driver travels over a bridge with expansion gaps spaced 5.5m apart. At a speed of 12.0m/s, the car bounces up and down with exceptionally large amplitude. Two more 80kg passengers now get in the car. a) What speed will result in maximum...