Shm Definition and 502 Threads

MENTOR Note: Thread moved here from Classical Physics hence no template I have a question set that I need to be able to answer before my exam next month, I know how to answer all of them except this one. I get the feeling I'm being an idiot. Show that the simple harmonic motion solution of the...

Homework Statement Two point masses m1 and m2 are coupled by a spring of spring constant k and uncompressed length L0. The spring is fully compressed and a thread ties the masses together with negligible separation between them. The tied assembly is moving in the +x direction with uniform speed...

Homework Statement Some sand is sprinkled onto the cone. The sand oscillates vertically with the frequency of the cone. The amplitude of oscillation of the cone is increased. At a particular amplitude of oscillation the sand begins to lose contact with the cone. By considering the forces...

So I'm trying to figure out how we got the allowed vibrational energy levels for a diatomic molecule by approximating it with simple harmonic motion. I do know how to use the uncertainty principle to get the zero-point energy: We know that the potential function is ##V(x) = \frac{1}{2}mx^2##...

<< Mentor Note -- thread moved from the technical forums, so no HH Template is shown >> Hello, So I've been doing old practice questions on SHM to revise, and just been frustrating myself on this one for a bit. The question is: "An object vibrating with simple harmonic motion has a maximum...

Homework Statement A particle performs S.H.M. with amplitude 25 cm and period 3 s. The minimum time required for it to move between two points 12.5 cm on either side of the mean position is ? Homework Equations ##y##=##a## ##sin####w####t## The Attempt at a Solution Solution is ##y##=a sin...

Homework Statement A mass m at the end of a spring oscillates with a frequency of 0.84 Hz . When an additional 730 g mass is added to m, the frequency is 0.65 Hz . Homework Equations f*2pi = w w = (k/m)^1/2 f = (1/2pi)*(k/m)^1/2 The Attempt at a Solution I simply used the third equation...

Homework Statement [/B] Two cities are connected by a straight underground tunnel, as shown in the diagram. A train starting from rest travels between the two cities powered only by the gravitational force of the Earth, F = - \frac{mgr}{R}. Find the time t_1 taken to travel between the two...

For the lab I have to find the spring constant and how force relates to time with simple harmonic motion. To find the spring constant, I used hooke's law and compared different added masses to the stretch from the equilibrium position. When I graphed that, the slope was the spring constant since...

1. Homework Statement Homework Equations KE=½m(ωa)2 The Attempt at a Solution So first I did this: 2.4x10-3= ½ mω2(1.5x10-2)2 To find mω2=21.33 And substitute that into the KE eqn to find the new amplitude, which is 1.30x10-2 But I only did that because that was the only way I could think...

Homework Statement An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V0 and its pressure is P0. The piston is slightly...

If I have a system where the following is found to describe the motion of three particles: The normal modes of the system are given by the following eigenvectors: $$(1,0,-1), (1,1,1), (1,-2,1)$$ How can I find the corresponding eigenfrequencies? It should be simple... What am I missing?

Homework Statement A metal rod of length ‘L’ and mass ‘m’ is pivoted at one end. A thin disc of mass ‘M’ and radius ‘R’ (<L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its centre and (case B) the...

Homework Statement A rod attached to a ceiling at one end and a disc on the other end is performing SHM. In case (1) the disc cannot rotate. In case (2) the disc can rotate about its centre. Compare the restoring torque and angular frequency in both cases. Homework Equations...

Homework Statement I am taksed with putting some simple harmonic motion (in this case linear harmonic motion) into graphs. For my first graph, I am graphing theta vs. time and analyzing three different numerical methods for the solution (Euler, Euler-cramer, Runge Katta). For my second graph...

I have some difficulties regarding oscillation and SHM, i hope someone makes it clearer to me. Firstly, I don't have a good intuition of the formulas for velocity and acceleration as functions of time. I have no idea why the negative sign is present in the formula and what it's supposed to mean...

Homework Statement Verify that Ae^(-βt)cos(ωt) is a possible solution to the equation: d^2(x)/dt^2+ϒdx/dt+(ω_0)^2*x = 0 and find β and ω in terms of ϒ and ω_0. Homework Equations N/a, trig identities I suppose. The Attempt at a Solution I think this is simply a 'plug and chug' type...

In an SHM, the only force that should be acting, that is the net force should be the restoring force F, by definition... F = -kx For example there is a massless spring of spring constant k attached to the ceiling and there is a body of mass m hung at it and avoiding all kinds of friction...

How does one arrive at the following equation to approximate spring constant for solids... using Hooke's Law F ∝-x ⇒ F = -kx and strain∝stress ? k = (m/a2) × (K/ρ)½ where k≡spring constant m ≡ mass of a single atom a ≡ atomic spacing K ≡ bulk modulus ρ ≡ density

In Simple Harmonic Motion, can (k/m) = ω2 be expressed for all SHMs or only the ones in which the mass due to which the SHM is being executed is performing a circular motion? Since for example, in the case of spring, there is no circular motion involved, so omega should not be defined for...

in shm,if minimum potential energy of an shm is not zero,does that mean that in mean position ,spring is stretched. eg mass attached to a vertical spring.

I find most textbook explanations of resonance lacking. My understanding is that resonance occurs becuase less "driving energy" is lost when the driven frequency approaches the natural frequency of a system. But why does the energy loss curve like this? Since Q-factor is different for each...

Homework Statement A 4.0kg block is suspended from a spring with force constant of 500N/m. A 50g bullet is fired into the block from directly below with a speed of 150m/s and is imbedded in the block. Find the amplitude of the resulting simple harmonic motion. Homework Equations F=-kx...

Homework Statement Is the statement cirrect: "the rate at which a wave transfers energy depends on the amplitude at which the particles of the medium are vibrating." And does the energy=A^2 ? Homework Equations E (proportional) A^2 The Attempt at a Solution For the statement I am about...

Homework Statement I've attached an image of the problem question, it's Q1 I'm working on This is what I have so far: we have two components of SHM, position x and velocity v. when x = 0, v = a maximum, when v = 0, x = a maximum this is represented by sin & cos functions. where x =...

Homework Statement We take a horizontal copper bar with length of 20cm and attach it from the middle to a vertical spring which mass is neglected and has a spring constant K, we apply a horizontal magnetic field with magnitude 1/2 T and have a 10A current run in the copper bar. The bar rests...

Homework Statement The displacement of a machine is given by the simple harmonic motion as x(t) = 5cos(30t)+4sin(30t). Find the amplitude of motion, and the amplitude of the velocity. Homework Equations x''(t) = -4500cos(30t)-3600sin(30t) The Attempt at a Solution [/B] I should note that...

What is the difference between simple harmonic motion and oscillation?

Why is it that ## y = A\sin (\omega t + \phi) ## whereas ## x = A\cos (\omega t + \phi) ##? Why is it that the y function is a sine wave, whereas the x function a cosine wave? I'm sorry if this question sounds ridiculous.

For SHM of oscillating pendulum, when the pendulum is at the extreme position, what is considered as the displacement? The curve/arc of the circle the bob is following or the straight line distance from the mean position?

Why do we simply add the equations of SHM in case the two SHMs are superimposing?

In deriving wave equation or power transmission of wave transmitted by a string, it is usually stated (with some assumptions) that the transverse force on a point of the string is proportional to the slope at that point. An example is given in p.20 of this notes...

Homework Statement One end of a spring is attached to a wall to a block of mass X= 2kg (on a frictionless horizontal table). Another mass M of 150g moving at a speed of 7m/s collides (inelastic). This takes 0.4s to compress the spring to its max compression. I have to find the max force of...

Normally in high school physics-textbooks, the following formula for the period of simple harmonic motion (SMH) for a object on a spring is derived: T2= 1/(4π2k)*m where T is the period, k the springconstant and m the mass of the object on the spring. This is usually acquired by setting up a...

Hello, I am working in Papua New Guinea where there is a great deal of seismic activity. I am interested in using MS Excel for simulation of SHM due to seismic waves. To investigate the how frequency and wavelength of the waves affects buildings. Does anyone have any experience of this type of...

Homework Statement Where would be the perfect place to place a fiducial marker in a: mass on a spring system (vertical) and a simple pendulum? Homework EquationsThe Attempt at a Solution My teacher told me that for a simple pendulum it would be below the bob at equillibrium position because...

Hi, I'm very confused about one question in my homework, that is due today. I appreciate any help.Thank you very much. 1. Homework Statement The motion of a particle is given by: x = (6.0m) cos(0.586t + 0.72) Find the phase at time t=1.38s 2. Homework Equations Simple harmonic motion The...

Homework Statement 1. Harmonic Oscillator on Earth Gravity : In class, we solve the Harmonic Oscillator Problem, with a potential $$ V(x) = \frac{m ω^2 x^2}{2} \quad (1)$$ with ##ω = \frac{k}{m}## being the classical frequency. Now, assume that x is a vertical direction and that we place...

Homework Statement Homework Equations the equation is given in the question The Attempt at a Solution i tried replacing the 2/3 pi rad as the cos argument and i obtained 2. but the mark scheme says that the position is 3cm above AB. in the next part, we have a phase diff of 4/3 pi and i...

Mathematically, in SHM,why is x'' (acceleration) always in the direction if x increasing? So if he have a simple setup, an elastic spring on a smooth horizontal table, one end attached to a fixed point, the other to a particle. Let's say the fixed point is at the left end of the spring. If we...

Homework Statement A spherical ball of mass M and radius r rolls without slipping in a cylindrical of radius R .Find the time period of small oscillations .Homework EquationsThe Attempt at a Solution Please have a look at the picture attached . The ball moves to the right and upward, and...

Homework Statement In the figure mA = mB = 1kg . Block A is neutral while qB = -1C, sizes of A and B are negligible. B is released from rest at a distance 1.8m from A . Initially springs is neither compressed nor elongated. https://brilliant.org/discussions/thread/amplitude-of-oscillation/ View...

For a mass-spring system, Period, T = 2pi * root(m/k) So using hookes law, F = kx But if the spring is being stretched by a mass due to gravity, mg = kx So, k = mg/x But then this means, Period, T = 2pi * root(mx / mg) or, T = 2pi * root(x / g) Where have I gone wrong? I've been told...

I've always just accepted that as you scale down a mechanical system the frequency and Q factor both increase. For example, this Wikipedia page simply says that "Small bells ring at higher frequencies than large bells". But for a driven damped harmonic oscillator, what is the exact relationship...

Homework Statement Investigating the effect of mass on the period of oscillation. This experiment is about SHM of a floating cylinder, and the theory is explained in this website: http://physics.stackexchange.com/questions/64154/shm-of-floating-objects Also, I'm attaching a diagram of my...

Homework Statement A spring of stiffness k is attached to a wall and to the axle of a wheel of mass m, radius R, and moment of inertia I = βmR^2 about its frictionless axle. The spring is stretched a distance A and the wheel is released from rest. Assume the wheel rolls without slipping. At...

A particle moves such that its acceleration is given by: a = -β(x-2). Here β is a positive constant and c is the distance from origin What is the time period of oscillation for the particle? Solution: a = 0 at x = 2 (mean position) a = -βX where X = x-2. So, ω2 = β ⇒ T = 2π/ω = 2π/√β My...

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 Derive Newton's and Lagrange's equation of motion for the system. Discuss differences and show how Newton's equations can be reduced to lagrange's equations. Assume arbitrarily large θ. The system is a pendulum consisting of a massless rod of length L with a mass m...

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...