Harmonic motion Definition and 1000 Threads

I translated it, so the notation may not be so great. You have a vertical spring with a spring constant of 16 N.m^-1, we attach to its lower end a body with a mass of 0,4 KG and form a system which oscillates on a straight line with length of 8cm, we assume that at the start of the time, the...

Homework Statement A 4.00kg block is suspended from a spring with k = 500N/m. A 50.0g bullet is fired into the block from directly below with a speed of 125m/s and becomes embedded in the block. a) Find the amplitude of the resulting SHM. b) What percentage of the original kinetic energy of...

Homework Statement No friction. m3=5m, m2=12m, m1=3m Prove that the system's acceleration when it's released is a=0.2g. is it the max acceleration? Show that the equilibrium point is at x0=0.75L Show that the kinetic energy of the system is E=mgL Show that m2 will stop momentarily at...

A simple harmonic oscillator consists of a block of mass 45 g attached to a spring of spring constant 240 N/m, oscillating on a frictionless surface. If the block is displaced 3.5 cm from its equilibrium position and released so that its initial velocity is zero, what is the phase constant, φ ...

A 12kg mass undergoes simple harmonic motion with an amplitude of 10cm. If the force constant for the spring is 320N/m: a) Calculate the total energy of the mass spring system. Et=½kA^2 =½(320N/m)(0.1m)^2 =1.6 Jb) Calculate the maximum speed of the mass. Et=½mv^2 + ½kx^2 1.6 J = ½(12kg)v^2...

Homework Statement Two positive charges +Q are affixed rigidly to the x-axis, one at x = +d and the other at x = -d. A third charge +q of mass m, which is constrained to move only along the x-axis, is displaced from the origin by a small distance s << d and then released from rest. (a) Show...

V=Vo √1-(x^2/a^2) X is the distance of the spring's stretch, but how would you rearrange the equation if you are looking for Amplitude? They both use the same units (meters) as far as I am concerned. Help would be appreciated, thanks; I am still a beginner with Physics.

Homework Statement Can I get help in part (b) of this question ? Homework Equations KE=1/2 m v2 v= (2π f )√(A2 - x2) The Attempt at a Solution I substituted the second equation into first one, so i got KE= 1/2 m (2π f )2 (A2 - x2) but then couldn't complete

1. The balance spring of a watch is a hoop 1.2 cm in diameter, with a mass of 0.65 g. If the watch is running 45 seconds per day too fast, by what percentage should the rotational inertia of the hoop be changed? 2. Homework Equations : I = mR^2 Ia = -k(theta) x(t) = Xm Cos(wt + @) (just using @...

A 350-g mass is attached to a spring whose spring constant is 64 N/m. Its maximum acceleration is 5.3 m/s2. What is its maximum speed? So, i had a go at the question which basically required the knowledge that maximum acceleration occurs when displacement is maximum and maximum velocity occurs...

Homework Statement Hi Guys, This is the first exampe from Engel's problem solving book. After a long period of no math I am self studying. I do not know where my knowledge deficits lie, and was recommended this site for help. "E1. Starting with a point S (a, b) of the plane with 0 < b < a...

Homework Statement An 8.0 lb block is suspended from a spring with a force constant of 3.0 lb/ in. A bullet weighing 0.10 lb is fired into the block from below with a speed of 500 ft/sec and comes to rest in the block. a) Find the amplitude of the resulting simple harmonic motions b) What...

Homework Statement My textbook states that for simple harmonic motion, the sinusoidal graph of the x (displacement) as a function of time can be created using the "Equation of motion". Homework Equations The equation of motion ##A \cos (\omega t + \phi)## The Attempt at a Solution I know...

Hello, I was asked by my professor today to graph the motion, as well as the energies, of a spring that undergoes driven and/or damped oscillation; however, I was unable to because I do not have a very good idea of how they work. Can someone explain to me, qualitatively, what it means to have a...

Homework Statement Compare the simple harmonic motion of two identical masses oscillating up and down on springs with different spring constants. Homework Equations F = -kxThe Attempt at a Solution Okay, so I understand that the higher the spring constant, the harder it is to compress the...

Homework Statement A particle moves with simple harmonic motion in a straight line with amplitude 0.05 m and the period 12 s.Find (a) the maximum speed , (b) the maximum acceleration of the particle.Write down the values of the constants P and Q in the equation x/m = P sin [Q)(t/s)] Homework...

Homework Statement I am curious as to how the second line in the equation is equal to the third line in the equation. The book my class is using is Taylor and it just skips so many steps. What happens to the sign, I know this must relate to euler in some way I am just not sure how. Thank you...

Homework Statement A 0.500Kg object is undergoing simple harmonic motion at the end of a horizontal spring with force constant k=300N/m. When the object is 0.012m from the equilibrium position, it is observed to have a speed of 0.300m/s. What is: a) The total energy of the object at any point...

Homework Statement A 50g mass is attached to a spring and undergoes simple harmonic motion. It's maximum acceleration is 15m/s and maximum speed is 3.5m/s. Determine a)angular frequency, b) spring constant, c) amplitude. Homework Equations ω = √k/m X(t) = A*cos(ωt + ∅) The Attempt at a...

Homework Statement Homework EquationsThe Attempt at a Solution Suppose mass of platform is ##M_1## and that of coin is ##M_2## . The normal force between them is N . EOM for platform (mass M1) = ##-kx+M_{1}g+N = M_{1}\ddot{x}## EOM for coin(mass M2) = ##M_{2}g-N = M_{1}\ddot{x}## This...

Hi, I have a few questions relating to the equation for maximum acceleration for SHM: amax = A (2 x pi x f)^2 where amax = max. acceleration, A = amplitude, f = frequency. How are these variables supposed to be interpreted when you relate them to each other. For example, is A inversely...

Hi everybody, I'm writing an exploration on the mathematics of simple harmonic motion and I stumbled across something I fail to understand in one of my resources (http://tutorial.math.lamar.edu/Classes/DE/Vibrations.aspx). In the example the author uses toward the end of the resource, the...

Homework Statement Prove that: x=8sin2t+6cos2t is undergoing S.H.M. (Not too sure about how to prove for solution.) Homework Equations Solution for S.H.M. x=asin(nt+α) is \frac{d^{2}x}{dy^{2}}=-n^2xThe Attempt at a Solution...

Homework Statement A mass on a spring has an angular oscillation frequency of 2.56 rad/s. The spring constant is 27.2 N/m, and the system's kinetic energy is 4.16 J when t = 1.56 s. What is the oscillation amplitude? Assume that the mass is at its equilibrium position when t = 0.a. 63.1 cm b...

Homework Statement What length must the pendulum be changed to in order to show the correct time? L=0.5m After 12hours the clock is behind by 30minutes. Homework Equations w=sqrt(g/L) w=2πf The Attempt at a Solution I thought if I set the frequency equal to 1Hz and solved for length it would...

Homework Statement A mass m = 750 g is connected to a spring with spring constant k = 1.5 N/m. At t = 0 the mass is set into simple harmonic motion (no damping) with the initial conditions represented by the point P in the phase space diagram at the right. **(This phase space diagram has...

Homework Statement A harmonic potential is parameterised as: V(x)=\frac{k}{2}(x-x_{0})^2An object moves within this potential with a total energy E > 0. (i) Where are the two turning points of the motion xA and xB? (ii) Write down the equation of motion for the object, and use it to find...

Homework Statement http://i.imgur.com/u8vUv5a.jpg Find the phase constant. Homework Equations x(t)=Acos(ωt + Φ) v(t)=-Aωsin(ωt + Φ) Vmax = ωA ω=2π/T The Attempt at a Solution ω = 2π/12 = 0.5236 A = 60/0.5236 = 114.59 cm v(0) = -30 = -114.59(0.5236)sinΦ 0.5 = sinΦ Φ = π/6 and 5π/6. Which...

Homework Statement The position of a 50 g oscillating mass is given by x(t)=(2.0cm)cos(10t−π/4), where t is in s. If necessary, round your answers to three significant figures. Determine: The total energy. Homework Equations T = 2π/w T = 2π√m/k 1/2kA^2 1/2mv^2 1/2kx^2 The Attempt at a Solution...

Homework Statement I have a question about simple harmonic motion: Where it says " if we denote the ratio k/m with the symbol omega squared ... ": I know it says that they chose omega squared to make the solution simpler, but I mean, to me it doesn't really make sense. Omega is associated...

Consider a vertical pendulum affected by gravity (See the pdf file i included). Now i can choose two different opposite directions for my unit vectors which give me different equations. \downarrow : m\ddot x = mg-kx \uparrow : m\ddot x = kx-mg Which of course makes perfect sense, changing...

Homework Statement A mass m is sliding back and forth in a simple harmonic motion (SHM) with an amplitude A on a horizontal frictionless surface. At a point a distance L away from equilibrium, the speed of the plate is vL (vL is larger than zero). Homework Equations What is the period of the...

Hi pf. I have a question about an experiment. If you lie a ruler horizontally across two supports (one near each end) and then hang a weight in the middle it will undergo SHM if you pull the mass down. If you move the supports in closer it will oscillate with a higher frequency. I just wanted to...

Homework Statement So I have to write a report based on an experiment that I have conducted. I know that my report is connected with Simple Harmonic motion and Elastic force, but I do not know how to describe it in a more efficient/scientific way. Essentially, I am dropping a weight (constant)...

*note: my previous thread will be deleted because I didn't include relevant equations + I put two unrelated problems in the same thread. 1. Homework Statement A cat bobble head doll consists of a weighted head on top of a spring. When the head hangs straight sown in equilibrium, it is observed...

Homework Statement [/B] A mass-spring system is oscillating with an amplitude of 10.0 cm. What is the speed of the mass at a location where the kinetic energy of the mass and the potential energy of the spring are equal? I want to know if it's possible to solve for just a number, that is, not...

I did an experiment at school, and the experiment SET UP that i did is basically shown in the word attachment link. http://www.schoolphysics.co.uk/age16-19/Mechanics/Statics/experiments/bending_of_a_beam.doc. I have two questions! Question 1:when i did the experiment, I found that with a...

I know this is simple, but I don't fully understand why the motion of a piston is considered to be simple harmonic? Wouldn't the piston and connecting rod have mass?

Homework Statement A horizontal plank of mass m and length L is pivoted at one end. The plank's other end is supported by a spring of force constant k (see the figure below). The plank is displaced by a small angle θ from its horizontal equilibrium position and released. Find the angular...

Homework Statement One end of a light hacksaw blade is clamped in a vise with the long axis of the blade horizontal and with the sides vertical. A 0.665- kg mass is attached to the free end. When a steady sideways force of 20.5 N is applied to the mass it moves aside 13.3 cm from its...

Given a position vs time graph of simple harmonic motion of an object and using the equation x(t) = xo = A sin (ωt +Φ), how am I supposed to find Φ? I can easily find A and the period (T). I also know T = 2 pi / ω, so I can find ω. But I don't know x(t) and t. I tried finding random points in...

For one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, could be obtained by means of Newton's second law and Hooke's law and i don't get this part which...

Homework Statement Homework Equations acceleration = -(2*pi*f)^2 * x, where f is the frequency and x is the displacement from equilibrium. The Attempt at a Solution I thought the acceleration would be greatest when the displacement from equilibrium is greatest, so at point P, but the answer...

Homework Statement http://puu.sh/cAjmp/14ba3df23a.jpg Homework Equations Acceleration at any instant: -(2*pi*f)^2 * x, where x is displacement from equilibrium and f is frequency. The Attempt at a Solution Firstly, I know it can't be D as acceleration would increase as potential energy...

Homework Statement [/B] Write the second-order equation for the harmonic oscillator, y ̈ + ω2y = 0 as two linear ordinary differential equations. What is the analytic solution y(t) if ω = 2π, y(0) = 1 and y′(0) = 0? Homework EquationsThe Attempt at a Solution So, I have to write some...

Homework Statement Actually this is not a problem. This is about something i couldn't understand. Homework Equations where wt equals θ The Attempt at a Solution I can understand that x=r.cosθ it is obvious. But i can't understand why Vx=-V.sin(w.t) When i take a triangle from that...

Homework Statement I solved this physics question, but I am unclear about why Amplitude was the amount the spring was stretched by (which should be the new equilibrium point), instead of the amount the person pulled the mass down by (which should be the amplitude). Can anyone help? On your...

Homework Statement A simple pendulum of length =30.0cm is released from rest from an angle of θ=10.0∘ to the vertical. Assuming that the pendulum undergoes simple harmonic motion, find its maximum speed. Source: https://isaacphysics.org/questions/accuracy_shm_pendulum_num Homework Equations a)...

Homework Statement A mass on the end of a spring is released from rest at position x0. The experiment is repeated, but now with the system immersed in a fluid that causes the motion to be critically damped. Show that the maximum speed of the mass in the first case is e times the maximum speed...

Homework Statement Explain the shape of the velocity-displacement and acceleration-displacement graphs for an object undergoing simple harmonic motion. The graph is attached to this thread Homework Equations v = wsqrt(A^2-x^2) where w = angular frequency, A = amplitude and x = displacement...