Mass-spring system Definition and 45 Threads

This looks like a classical setup but I can't find a solution. We can calculate the energy of the system by looking at the work done by the gravity and the spring. But how do we divide the energy between the kinetic energy of the pulley and the rotation of the pulley?

I understand the derivation of T= 2π√m/k is a= -kx/m, in a mass spring system horizonatally on a smooth plane, as this equated to the general equation of acceleration of simple harmonic motion , a= - 4π^2 (1/T^2) x but surely when in a vertical system , taking downwards as -ve, ma = kx - mg...

For the maximum elongation the velocities of the blocks should be equal. With that i used two conservation of energy for m1 and m2, for m1 the work of the elastic force is integral of kx(dx1) and for m2 kx(dx2), where X1+x2=x. I got three equation and four variables since i don't know the final...

$$m_1 \ddot{x} - m_1 g + \frac{k(d-l)}{d}x=0$$ $$m_2 \ddot{y} - m_2 \omega^2 y + \frac{k(d-l)}{d}y=0$$ It is two masses connected by a spring. ##d=\sqrt{x^2 + y^2}## and ##l## is the length of the relaxed spring (a constant). What is the strategy to solve such a system? I tried substituting...

I am confused by this question and was hoping someone could clear this up for me, I know this is simple. A mass-spring system vibrates at 10 Hz. Ideally, i.e., without friction, it would continue forever at the same amplitude. In practice, its amplitude is found to decay such that it decreases...

A mass-spring system is in free vibration after an initial excitation. There are no outside forces acting on the system. What is the value of the spring stiffness k (units of N/m; round your answer to a single decimal place)? Mass m = 0.6 kg Amplitude A = 0.4 Using this equation: z(t) = A sin...

Homework Statement Given the IVP \ddot{r}+\dot{r}+20r=0\\ r(0) = 0.8\\ \dot{r}(0) = 0 for the length of an oscillating spring (damped), we find that the general solution is r=e^{-0.5t}[0.8\cos(\sqrt{19.75}t)+\frac{0.4}{\sqrt{19.75}}\sin(\sqrt{19.75}t)] and I wish to find the curve bounding...

Homework Statement We know that after long run of simple mass-spring system, there should be a probability of finding the mass at certain points between -A and A.. Obviously in probability of finding the particle near A or -A is higher than finding the particle at 0, because the speed is the...

Homework Statement Problem: [/B] Given the mass spring system solve for k1 The natural frequency wn = 10 s-1 k1=2k2 m=1kg Homework Equations wn=(k/m).5 The Attempt at a Solution solve for k1 m x w2n =2.5k1 k1 = 40 N/mNote: I calculate 40 N/m and the solution states 250 N/m. I think I...

[Mentor's note: Thread title changed to reflect question content] I really need some help with this one: 1. Homework Statement An unhappy rodent of mass 0.307kg , moving on the end of a spring with force constant 2.48N/m , is acted on by a damping force Fx=−b⋅vx. Part A If the constant b has...

Homework Statement Suppose the surface is completely frictionless. Will the spring experience any length change?[/B]Homework EquationsThe Attempt at a Solution To change the length of the spring, force should be applied from both ends. In this case, there is no force of friction. So, my...

1. A 1 kg block is on a flat frictionless surface. Attached to a relaxed spring (k=50N/m). A light string is attached to the block and runs over a frictionleas pulley to a .45kg dangling mass. If the dangling mass is released from rest, how far will if fall before stopping? Homework Equations...

Case of a spring with a mass,m, that has been stretch beyond the equilibrium in the positive x direction. mg + (-kx0) = 0 k = mg/x0 stretch: F = mg+ [-k(x0+x1)] = mg-kx0-kx1 but since mg-kx0 = 0 F = 0-kx1 = ma ma = -kx1 a = -kx1/m How do I arrive at the corollary from a = -...

hi, all. I am trying to derive the equation of motion of a mass spring system without using the energy method but I am wrong somewhere and I can't find it, can you help me find where I am wrong. Equation of motion of a simple mass spring system is indeed mx''+kx=0 but here I am thinking that...

Homework Statement Find the steady-state motion of the mass–spring system modeled by the ODE: 4y''+12y'+9y=225-75sin(3t) Homework Equations for a diff eq modeled as: my''+cy'+ky=F0cos(ωt), yp=acos(ωt)+bsin(ωt) a=F0*(m(ω02-ω2))/(m2*(ω02-ω2)2+ω2c2) b=F0*(ωc)/(m2*(ω02-ω2)2+ω2c2)...

Picture of the system (it's sideways): http://tinypic.com/r/28qq4pi/5 Consider the mass from the spring in the figure. Let m=1, k=1, and g=9.81. Assume that x and y are zero when the 2 springs are unstretched. Assume the system starts from rest with the first spring extended by an amount...

Homework Statement Homework Equations The Attempt at a Solution Well since spring is in SHM, only conservative forces are at play here. So using conservation of energy, the kinetic energy would be the change in potential energy. Which I have set up as KE = 1/2k(A^2)2 -...

Homework Statement A mass of 122 g is attached to a vertically hung spring. The mass stretches the spring 13.8 cm. (a) What is the spring constant of the spring? (b) If the mass is dropped from rest from a position where the spring is just relaxed, what will be the maximum distance the...

Homework Statement This is a horizontal mass spring system in a simple harmonic motion problem set. Vmax = 20 m/s F = 10 N m = 0.5 kg Find Amplitude (A) and spring constant (k) Homework Equations The Attempt at a Solution I could not figure out a way to solve this problem, and the only...

I am reviewing for a final and I don't know how an impulse affects the differential equation for motion in this mass-spring system. Can someone please help? A mass m=1 is attached to a spring with constant k=2 and damping constant c=2. x(0)=0 & x'(0)=0. At the instant t=π, the mass is struck...

A lot of problems I see have vertical mass-spring systems, where a mass m hangs from a spring with spring constant k stretching it a distance D, and usually all but one of those quantities is known. But would you equate the forces or the energies, i.e. which is the correct equation to use: mg=kD...

Could somebody help me in deriving the following expressions? I can judge that the first equation is a common expression for finding Keq for a mass-spring system in series.. Can't do the rest :/ anybody please ? Thanks in advance.

Homework Statement A certain spring elongates 9mm when it is suspended vertically and a block of mass M is hung on it. The natural frequency of this mass-spring system is: a)0.014 b) 5.3Hz c) 31.8Hz d) 181.7 e) need to know M x=9mm mass=M Homework Equations I don't know any...

A spring is mounted at an angle of theta = 39degrees on a frictionless incline as illustrated in the figure below. The spring is compressed to 15 cm where it is allowed to propel a mass of 4.9 kg up the incline. (a) If the spring constant is 580 N/m, how fast is the mass moving when leaves...

Homework Statement Given a transfer function in the Laplace Domain Detemine an expression for x(t), given f(t) is a sinusodial input with frequency omega = root(k2/m2) and amplitude of 1 N (initial conditions equal 0)Homework Equations...

Homework Statement Mass m attached to spring with spring constant k=Am. It feels a resistive force magnitude Bmv where v is the speed. and A, B are constants such that 4A > B^2 What is the fractional change in amplitude of oscillation in one complete oscillation? Homework Equations...

Homework Statement A spring is mounted at an angle of = 38 on a frictionless incline as illustrated in the figure below. The spring is compressed to 15 cm where it is allowed to propel a mass of 5.4 kg up the incline. If the spring constant is 565 N/m, how fast is the mass moving when leaves...

Homework Statement I have a 2D isotropic mass-spring system. The mass is pulled a distance A=1m, and then given an upwards kick with a velocity v_0. The k=1, m=1kg. I need to find the furthest distance from the origin the mass will travel in its orbit. Homework Equations x(t)=A_x\cos(\omega...

[FONT="Arial Black"]Beats and Resonance In the Beat not have friction force, correct ? m \frac{d^2x}{dt^2} + kx = F_o cos(wt) We can write as \frac{d^2x}{dt^2} + w_o^2 x = \frac{F_o}{m} cos(wt) If w \not= w_o Assuming (Particular solution) x_p = acos(wt) + bsin(wt) Why we...

[FONT="Arial Black"]Damped vibration m \frac{d^2x}{dt^2} + \gamma \frac{dx}{dt} + kx = 0 Characteristic equation is mr^2 + \gamma r + k = 0 r_1 = \frac{- \gamma + \sqrt{( \gamma )^2 - 4mk}}{2m} r_2 = \frac{- \gamma - \sqrt{( \gamma )^2 - 4mk}}{2m} In overdamped ( \gamma )^2 -...

[FONT="Arial Black"]Vibration Free Please, are correct? m \frac{d^2x}{dt^2} + kx = 0 Where frequency is w = \sqrt{\frac{k}{m}} \frac{d^2x}{dt^2} + \frac{k}{m}x = 0 The characteristic equation is: r^2 + w^2 = 0 r = +or- iw where i^2 = -1 Then x(t) = C_1e^{iwt} +...

Homework Statement Hi guys/girls Professor gave this very simple homework where I need to convert the system below to a state-space model. The system itself is represented by the equation m*x" + k*x = f(t) Where m = 5 and k = 1. Note that, " (doublequote) is a second-order derivative...

Homework Statement A block of mass 1.2kg, resting on a horizontal surface of coefficient of kinetic friction of .15, is attached to a linear spring of force constant 12.0 N/m. When the spring is unstretched the mass is at a position x=0. THe mass is pulled to the right streching the spring a...

Simple Mass-Spring System Problem! A mass M slides across a frictionless horizontal table with constant speed V_0_. It collides with a spring of spring constant k, compressing it. The mass-spring system then rebounds. Take the position of the mass when it first hits the spring to be x=0. a)...

When trying to solve a problem I arrive at the following equation of motion / Hill equation: \frac{d^{2}y}{dx^2} + \frac{4 k_0}{m w^2} cos(2x)y = 0 There exists a value x_0 such that for all x>x_0 the motion is stable. I actually don't know what is meant by this 'stability'. Can...

does anybody know if the action of a real mas-spring system suspended vertically, support or refute the law of conversation of energy

A mass M slides across a horizontal table. It collides with a spring, compresses the spring, and then the mass-spring system rebounds. This system can be used to find the spring constant k. When the mass first hits the spring at x = 0, it has speed v0. a.) Let the coefficient of kinetic...

Homework Statement You have a forced, mass-spring system, without damping. Spring constant = 4 N/m weight of mass = 9.8 N mass = 1 Kg Find the motion X(t) of the mass if ω = 1.5 (Hz) and deduce the maximum elongation of the spring. Sketch the vibrations X(t). Do same for ω = 1.9, 3. Find...

Homework Statement A 250 g block is resting on a frictionless horizontal surface. The block is attached to a spring. The mass-spring system is compressed by a 2.5 N force and then released from rest. (a) The resulting oscillation has a 1.0 s period. What is the spring constant? (b) What is...

I need help in finding the equations that describe this system. http://img530.imageshack.us/img530/2584/44567537be2.jpg Any help will be appreciated. Thank you, Kfir

1. Homework Statement and 2. Homework Equations Find position/velocity of a mass m attached to a spring of constant k when subjected to an oscillatinf roce F(t) = F sin(Bt) With B\not = \sqrt{k/m} The Attempt at a Solution Model; mx'' + kx = F \sin(Bt) I have no...

An object of mass m is traveling on a horizontal surface. There is a coefficient of kinetic friction, mu , between the object and the surface. The object has speed v when it reaches x=0 and encounters a spring. The object compresses the spring, stops, and then recoils and travels in the opposite...

Hey, Stuck on finding the mechanical energy of a mass-spring system, my question is as follows > A mass-spring system oscillates with an amplitude of .026 m. The spring constant is 290 N/m and the mass is 0.50 kg, it asks for the mechanical energy in (J). and the maximum acceleration of the...

Here's the question: "An object of mass m is traveling on a horizontal surface. There is a coefficient of kinetic friction mu between the object and the surface. The object has speed v when it reaches x = 0 and encounters a spring. The object compresses the spring, stops, and then recoils and...