Simple harmonic motion Definition and 917 Threads

In lecture, we are beginning to learn about waves and periodic motion under simple harmonic motion. We were given the equations: x=Acosθ and θ=ωt+\phi -- Substituting, we get x=Acos(ωt+\phi). This is simple enough; however what is Phi? All I was told is that "phi is a constant that allows us...

Homework Statement I doubt energy is conserved in SHM, or it might be possible that i be doing something wrong. The particle (red dot) in the attachment is at its equilibrium position and oscillates with Simple Harmonic Motion between the two yellow colored plates. Amplitude A = 1.5 m...

Homework Statement Part (iv) The Attempt at a Solution My attempt is below. Is it correct ? Homework Statement

Simple Harmonic Motion (F=-kx) -- Help! Hello Ladies & Gentlemen please answer my question: Q: The formula for Hooke's LAW is Felastic=-kx , so, the "X" is always negative? And the "F" is always negative? I know the "K" is always should be positive but please explain to me because I'm confused...

Homework Statement A cheerleader waves her pom-pom in simple harmonic motion with an amplitude of .180m and a frequency of .850Hz. a) Find the maximum magnitude of the acceleration and of the velocity. b) Find the acceleration and speed when the pom-pom's coordinate is x=+.090m. c)...

In my physics class we're talking about LC and LRC circuits, and the equations are analogous to those for SHM. However, I don't see how x=Acos(ωt+\varphi) satisfies m(d^2x/dt^2)+(k/m)x=0. I've never done differential equations and in the book it seemed like the author just guessed and checked...

Homework Statement Homework Equations F=ma The Attempt at a Solution I did the first three parts . The last part of this question is quite hard, i tried using Newton's 2nd law of motion but ... here is what happens : T is the tension, as stated in the question . so the equation of...

Homework Statement So you're being pushed on a swing by someone who is whistling at a constant 60Hz. At the bottom, Vmax is 4 m/s. Explain what you hear as you swing toward and away from the source of whistling (speed of sound is 343 m/s for this problem). Homework Equations Observed...

Im kind of confused on which acceleration equation to use. A = -(kx)/m or A = -(w^2)Acos[(angular freq)(time) + phase constant] as both of these contribute to SHM. Im guessing I can use the first acceleration equation when i know how far the object stretched and if i don't i...

Homework Statement A mass m hanging on a spring oscillates vertically. If the equilibrium point of the oscillation is a distance d below the relaxed length of the spring and if the amplitude of the oscillation is A, what is the maximum kinetic energy of the oscillation?[b]2. Homework Equations...

what is the limitation of T = 2π \sqrt{\frac{m}{k}}

Homework Statement Not exactly sure why a time value of 0.500s is given, but I am positive it is why my answer isn't correct: Q. a 1kg object is attached to a horizontal spring. The spring is initially stretched by 0.100m and the object is released from rest there. It proceeds to move...

Homework Statement We have U-shaped tube filled with liquid , if liquid is displaced through length 'x' find time period of SHM please help me :confused:

Homework Statement A massless spring hangs down from a support, with its lower end at y=0, where the y-axis is vertical and points downward (normal orientation of y). When a small unknown mass is attached to the spring, the lower end of the spring moves down to a position y_0 for the mass...

Homework Statement A meterstick is clamped to a tabletop. The end of the meter stick is deflected downwards a small distance x and is released such the end of the meterstick moves up and down in simple harmonic motion. The meterstick is measured to oscillate up and down 10 times in 5.0...

Homework Statement A 100g particle hangs freely at rest on the end of a spring of stiffness 10N/m. If the particle is projected upwards with a speed of 2m/s, find the time taken until it first comes to rest and the distance travelled. Homework Equations Well, there's F = -k.x and of course the...

It isn't making any intuitive sense. If it isn't moving in circular motion, how can it have angular frequency or speed? Also, v=\pm ω\sqrt { A^{ 2 }-x^{ 2 } } only applies to SHM with springs only, right? Also, does anyone know how to derive this equation below? x=\frac { \pm \sqrt { { { v...

Homework Statement Homework Equations F = -dU/dx The Attempt at a Solution U = \frac{1}{2}kx^2 + mgxsin\theta \\\\ F = -(kx + mgsin\theta) \\\\ F = -kx - mgsin\theta \\\\ We want to set the force = 0 because that's when the block is in equilibrium with no forces acting on...

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...

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...

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 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 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...