Shm Definition and 489 Threads

Homework Statement A mass-spring system with a natural frequency of 3.6 Hz is started in motion with an initial displacement from equilibrium of 6.1 cm and an initial velocity of 0.7 m/s. What is the value of ϕ? (Question aside: Finding the amplitude of the resulting function?) Homework...

Homework Statement According to an old model due to JJ Thompson, an atom consists of a cloud of positive charge within which electrons sit like plums in a pudding. THe electrons are supposed to emit light when they vibrate about their equilibrium positions in this cloud. Assume that in the case...

The goal is to measure the spring constant of a spring and then calculate a theoretical period of the oscillation and compare the results to a real life measurement. Extension of spring A: Neutral: 52 cm 1 N: 41 cm 2 N: 30 cm F = kx k = 9.1 N/m 10 oscilliations = 9.26 seconds Calculating the...

Homework Statement We have a cubical hollow box, edge length ##a## suspended horizontally from a frictionless hinge along one of its edges. The box is displaced slightly and undergoes SHM. Show that the period of the oscillation is given by ## T = 2\pi \sqrt{\frac{7\sqrt{2}a}{9g}} ## Homework...

Homework Statement The hand in (Figure 1) (a) holds a vertical block-spring system so that the spring is compressed. When the hand let's go, the block, of mass m, descends a distance d in a time interval Δt before reversing direction in (Figure 1) (b). Once the system comes to rest, the...

Homework Statement If the mass of a horizontal mass-spring oscillator undergoing SHM is 0.5kg and the force constant is 20N/cm, what is the maximum restoring force of the oscillator? And what is the maximum acceleration? (Time period is 6s and amplitude of oscillation is 12cm) Homework...

Homework Statement For a Particle executing SHM, the displacement x of the particle as a function of time is given as x=A sin 2 pi t, where x is in cm and t is in seconds. Let the time taken by the particle to travel from x = 0 to x =A/2 be t1 and the time taken to travel from x=A/2 to x = A be...

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 The question is: A simple pendulum is mounted in an elevator. What happens to the period of the pendulum (does it increase, decrease, or remain the same) if the elevator (a) accelerates upward at 5 m/s/s (b) moves upward at a steady 5 m/s (c) accelerates downward at 5 m/s/s...

Homework Statement a block of mass m as shown in figure lies on a smooth horizontal surface and springs are at natural length. when the block is displaced slightly then find the time period of oscillation Homework Equations $$T=2\pi\sqrt{\frac{m}{k}}$$ for series connection of...

Homework Statement A 50g block is attached to a vertical spring whose stiffness constant is 9N/m. The block is released at the position where the spring is unextended. What is the maximum extension of the spring? How long does it take the block to reach the lowest point? Homework Equations...

Homework Statement A plank on which a mass of mass m is put, is executing vertical SHM according to the equation y = sinωt + √3cosωt. At what time does the mass break of the plank and what is the value for the mass to break off ? Homework Equations The modified equation of motion looks like: y...

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...

Homework Statement A more sophisticated weighing machine contains two springs. The effect of these is that the machine is more sensitive to masses less than some fixed value M0 than it is to greater masses. The equilibrium displacement is alpha1*M when M<M0, and (alpha2+c) when M≥M0 , where...

A mass on the end of a spring which is hanging vertically is raised up and let go. It then oscillates between 2m and 1.5m above the floor and completes 32 cycles in one minute. The height, h metres, of the mass above the floor after t seconds can be modeled by the function h=acos(pi t / 180)...

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 block attached to a horizontal spring of force constant 75 N/m undergoes SHM with an amplitude of 0.15 m. If the speed of the mass is 1.7 m/s when the displacement is 0.12 m from the equilibrium position, what is the mass of the block? k = 75 N v = 1.7m/s @ 0.12m...

Homework Statement At time t, the velocity of v of an object undergoing simple harmonic motion at the end of a spring is given by the formula below. here m is mass of the object (in g), k is a constant depending on the spring (in g/s squared), a is the maximum distance the object moves and t...

Question: The damped frequency (f) is 100 Hz. The ratio of the amplitude of two successive maxima is one half. What is the undamped frequency? My first problem is I don't understand the basic equations I'm working with. If W is the undamped angular frequency and w is the damped frequency, I...

Homework Statement In a thread with a sphere of mass M on one end, another thread BC is suspended with a sphere of mass m (as the image below). The point A executes small oscillations in the horizontal of period T. Find the length L of BC, knowing that B remains straight underneath A at all...

[Note: Post restored from archive - gneill, PF Mentor] Homework Statement A pendulum consists of a uniform circular disk of radius r which is free to turn about a horizontal axis perpendicular to it's plane. Find the position of the axis for which the periodic time ( for small amplitude...

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I have a homework problem I need help with. I don't want the answer given to me since I know I can answer it with the proper guidance. How should I approach this problem? This is what I have so far. How should I approach this? Did I start off right? Thanks in advanced!

I have a homework problem I need help with. I don't want the answer given to me since I know I can answer it with the proper guidance. How should I approach this problem? This is what I have so far. How should I approach this? Did I start off right? Thanks in advanced!

Does anyone know how the mathematics/formulae of SHM (say a particle in a force field, with the standard a=-d) changes when the particle is given an initial velocity independent of the force causing SHM? For example in 1D say we have a graph of acceleration-displacement in the standard form...

When you compute the average potential energy of a horizontal spring mass system from the mean position to the positive amplitude A, the value comes to be (1/6)kA^2. For the average kinetic energy over the same range and direction, it is (1/3)kA^2, which is double the average potential energy...

Please look at picture. My textbook only gives the answer with -pi as a phase constant. But, since we are at "a switching point" on the unit circle, the sign doesn't really matter. The graphs give the same result whether a positive or negative sign is used. Am I right? Does it conceptually...

Q: During an earthquake, a skyscraper is designed to sway back and forth with simple harmonic motion with a period of 8 secs. The amplitude at the top floor of a particular earthquake is 70 cm. With respect to the simple harmonic motion of the top floor, calculate the following quantities: a)...

Homework Statement We set up a spring with a weight and displaced the spring from equilibrium position. Using a recording device and a motion sensor, we found various data that I have put in the attached table. When doing calculations for the lab, we ran into problems, but I simply want to...

Homework Statement A uniform steel bar swings from a pivot at one end with a period of 1.2 seconds. How long is the bar? Homework Equations T=2\pi\sqrt{L/g} The Attempt at a Solution I manipulated this equation to solve for L, giving me L=T^{2}g/4\pi^{2} Plugged in T=1.2 seconds...

Homework Statement The restoring force of a pendulum is F_\theta=-mg\sin\theta and is approximated to F_\theta=-mg\theta. The period is T=2\pi\sqrt{\frac{L}{g}}, but can be expressed as the infinite series: T=2\pi\sqrt{\frac{L}{g}}\left(...

Homework Statement A mass, m, attached to a spring hangs vertically downwards under gravity. It is subject to a viscous damping force proportional to its velocity. The spring constant is k > 0. A periodic force is applied to the spring and the equation of motion for the mass is \ddot x+...

Question; A 1 g mass is suspended by a spring and executes simple harmonic motion when released. At time t=0 the displacement is 40 cm and acceleration is -3.6 cm/s^2. What is the spring constant k? What is the maximum velocity of this mass? At what time would the modulus of the maximum velocity...

Homework Statement A 1.50 kg ball and a 2.00 kg ball are glued together with the lighter one below the heavier one. The upper ball is attached to a vertical ideal spring of force constant 165 N/m and the system is vibrating vertically with amplitude 15.0 cm. The glue connecting the balls is old...

Homework Statement A molecular bond can be modeled as a spring between two atoms that vibrate with simple harmonic motion. Figure P14.63 shows an SHM approximation for the potential energy of an HCl molecule. For E < 4 * 10^-19 J it is a good approximation to the more accurate HCl...

Question: This is question from A.P French vibrations and waves, problem 3-1 for anyone whom may have it An object of mass 1 g is hung from a spring and set in oscillatory motion. At t=0 the displacement is 43.785 cm and the acceleration is -1.7514 cm/sec^2. What is the spring constant? My...

Homework Statement A mass hanging on a spring is oscillating with SHM. The initial displacement due to gravity is 0.1m By considering the forces acting on the mass at equilibrium, calculate the angular frequency of the oscillations. Homework Equations \frac{d^2x}{dt^2} + {w}^{2}x = g...

The figure shows a U tube of uniform cross-sectional area A containing liquid of density p. The total length of the liquid column is L. When the liquid is displaced by an amount x from its equilibrium position, it oscillates with simple harmonic motion. The weight of liquid above AB provides...

Homework Statement A rectangular plate of sides ‘a’ and ‘b’ is suspended from a ceiling by two parallel strings of length L each. The separation between the strings is ‘d’. The plate is displaced slightly in its plane keeping the strings tight. Find the time period of SHM. Homework Equations...

Let's say there are 2 equations: (1) y(x,t) = A sin (ωt - ø) and (2) y2(x,t) = A sin (kx - vt) When are we interested in one over the other? Obviously, (1) tells us that y is represented in terms of ωt( 2πt/T) and ø. Whereas, (2) produces an equation stating the wave number, k(I tend to look...

Homework Statement A cube of mass m is connected to two rubber bands of length L, each under tension T. The cube is displaced by a small distance y perpendicular to the length of the rubber bands. Assume the tension doesn't change. Show that the system exhibits SHM, and find its angular...

I found this example in my physics textbook but it seems that the answers I get when I plug in the numbers are different to what the example says and I'm not so sure why?Image attached of course!It gives the phase as 7.5 which I got but when I used it in the equations I didn't get the correct...

Homework Statement Late correction, this is the 2008 F=ma exam: http://www.aapt.org/Programs/contests/upload/olympiad_2008_fnet_ma.pdf A mass is attached to the wall by a spring of constant k. When the spring is at its natural length, the mass is given a certain initial velocity, resulting in...

Homework Statement A particle is subjected to two simple harmonic motions given by x1=2[sin(100πt)] x2=2[sin(120πt+{π/3})] where x is in centimetre and time is in seconds. Find the displacement of the particle at t=1/80 Homework Equations The Attempt at a Solution The...

Homework Statement A 7kg weight is affixed to a spring with a constant of 327 N/m. System undergoing SHM. Position x is -1.22m and velocity of positive 3.54 m/s. The system then moves to a position where the velocity is positive 4.73. Find the position where the velocity is 4.73 m/s...

I apologize ahead of time for all of these post about oscillation. I am trying to learn this stuff on my own. I answered "a" because the x^2 function. But I don't know the second part.. Would it also be 3x^2 because it is proportional to the x(t) function?

I have a quick question about simple harmonic motion. My text states this in the picture attached, and I'm confused as to why: w(t+T) = wt+2pi wT=2pi I assumed w would distribute out into the first expression. I know this may be a dumb question but please help because it is bothering me...

Homework Statement A particle is simultaneously subjected to three SHM, all of the same frequency, and in the x direction. If the amplitudes are 0.25, 0.20, 0.15mm, respectively, and the phase difference between the 1st and 2nd is 45 degrees, and between the 2nd and 3rd is 30 degrees, find the...

Homework Statement Two identical simple pendulums of length 0.25m and period T, are mounted side-by-side. One is released from rest with an initial angular displacement of \displaystyle\frac{\pi}{12}rad, and the other is started with an initial angular velocity of 0.1 rad/s at θ=0. They are...

Hello, A was just helping my younger brother review some mechanics when I tried to explain how friction will cause the oscillations to eventually die out as the frequency keeps decreasing. So while analysing the force diagram and assuming that the frictional force is proportional to negative of...