What is Mass spring system: Definition and 55 Discussions

In a real spring–mass system, the spring has a non-negligible mass


{\displaystyle m}
. Since not all of the spring's length moves at the same velocity


{\displaystyle v}
as the suspended mass


{\displaystyle M}
, its kinetic energy is not equal to





{\displaystyle {\tfrac {1}{2}}mv^{2}}
. As such,


{\displaystyle m}
cannot be simply added to


{\displaystyle M}
to determine the frequency of oscillation, and the effective mass of the spring is defined as the mass that needs to be added to


{\displaystyle M}
to correctly predict the behavior of the system.

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  1. E

    I A Continuous Solution for Mass/Spring w/ Friction

    Suppose we have mass ##m## attached to spring with constant ##k##, and some coefficient of kinetic friction ##\mu## between the mass and the surface. Its displaced from equilibrium by some distance ##x## at ## t = 0 ##. I've come up with the following ODE to described ##x(t)## using the...
  2. S

    Derive angular frequency for mass spring system

    tried writing the x position as x = Acos(wt) (ignoring the phase) so that d2x / dt2 = -w2x Substituting that into the individual motion equations would get the required result for the individual masses, but I am not sure how to combine the equations to get the reduced mass
  3. T

    Does change in 'g' affect frequency of mass spring system?

    I attempted using f = 1/(2pi x sqrt l/g) For Earth I found the value of length to be 0.0276m. Then I substituted the value in the equation, putting (1/3)g instead of g, to find the value of f in Mars. My answer is C. I am confused. Please help me.
  4. LCSphysicist

    How to calc the period of this mass spring system?

    This is a problem very easy to deal with if we consider the effective spring constant, however, i want to avoid this solution, and see how to justify the period of this motion just by analyse the forces or the energy, what seems a little hard to me. First of all we would need to find the force...
  5. B

    Time period of a mass spring system

    I have attempted to draw a sketch of this but can't see how the data they gave me help to find time period This is what value I have ended up getting but I believe is wrong Much appreciated for any help!
  6. B

    AQA physics paper On potential energy in mass spring system

    The spring constant of a helical spring is 28 N mñ1. A 0.40 kg mass is suspended from the spring and set into simple harmonic motion of amplitude 60 mm. i use the equation 1/2 change in extension times by force where the force i assume is mass times by 9.8 but the mark scheme uses 1/2 kx ^2 and...
  7. F

    Maximum displacement in mass spring system

    Homework Statement A block is suspended by an ideal spring of the force constant K. If the block is pulled down by applying a constant force F and if maximum displacement of the block from its initial position of rest is X then, find the value of X. Homework Equations mg + F = XK + K(mg/K)...
  8. S

    Period of a mass spring system with 2 spring of same K(vert)

    A mass attached to a spring is oscillating in Simple Harmonic Motion. If an other spring of same sprinc constant is attached parrallel to the other spring, what is the period of this new system (as a function of the initial period). Here's what I did and have no idea if this is right: For the...
  9. Y

    Two masses connected by spring rotate around one axis

    Homework Statement Take the x-axis to be pointing perpendicularly upwards. Mass ##m_1## slides freely along the x-axis. Mass ##m_2## slides freely along the y-axis. The masses are connected by a spring, with spring constant ##k## and relaxed length ##l_0##. The whole system rotates with...
  10. A

    Potential energy in a Mass spring system

    Why is the rate of change of potential energy always same the rate of change of kinetic energy in a mass spring system? Additiinally, How do we determine the rate of change of potential energy in such case?
  11. A

    Energy changes in mass spring system

    Why is the kinetic energy vs time curve of a mass spring system is just a modulus of respective velocity time curve. How can we prove it mathematically ?
  12. Dusty912

    Simple Harmonic Oscillator: Mass Spring System

    Homework Statement [/B]A simple harmonic oscillator consists of a block of mass 2.00 kg attached to a spring of spring constant 100 N/m.When t =1.00 s, the position and velocity of the block are x =0.129 m and v =3.415 m/s. (a) What is the amplitude of the oscillations? What were the (b)...
  13. D

    So the title could be Finding Equilibrium in a Mass Spring System with Torque

    1. Homework Equations // Tension of the spring // Where sinL between `bottom right` of the spring and the bar Ft = sinL * kx // Where x0 is the initial length of the spring Ft = sinL * k(x - x0) // Force of gravity Fg = -mg // Find x0 // sqr = square root x0 = sqr(100^2 + 100^2) //...
  14. W

    Natural frequency of a mass spring system

    Homework Statement Homework Equations T = 2π√(m/k) mx'' + kx = 0 F = ma The Attempt at a Solution I don't honestly know where to start with this. I'm really out of my league in this class, and I'm trying my best to catch up with the things I didn't quite master in Dynamics and Physics... As...
  15. D

    Mass spring system - unknown spring constant

    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...
  16. A

    Understanding Dual Mass Spring System: Relating Acceleration and Oscillations

    Dear members I'am stuck in Dual mass spring system. How do we relate acceleration of masses when they are are oscillating relatively with let say amplitudes x1 and x2? Is there any simpler approach available please let me know.thanks.
  17. diracdelta

    Solving Mass Spring System Homework

    Homework Statement Starting from system of springs and masses (on picture), fina a force in x direction which n-th mass acts on n+1st mass, if harmonic wave ψ(x,t) is traveling in system. In equilibrium every mass is compressed i acts with force of F0 on masses. Consider a case in boundary of...
  18. H

    How to Calculate Work and Power in a Mass Spring System

    Homework Statement consider a mass spring system mounted on a horizontal surface. The left end of the spring is rigidly mounted, and the spring constant is 27 N/m. A block with a mass of 7 kg is placed on the right side of the spring and compresses the spring a distance of .15 m. The region on...
  19. S

    MHB Displacement of mass spring system

    The displacement y(t) of a driven mass-spring system is described by the differential equation 2y'' + 14y = 8 cos(2t) with initial value conditions y(0) = 0; y'(0) = 0. (a) Is this system damped or undamped? (b) Is this system resonant? (c) Write the solution to the IVP in terms of a product...
  20. D

    MHB Finding State Matrices for a Mass Spring System

    I am trying to find the state equations for a mass spring system. I found the transfer function to be \[ H(s) = \frac{X_1(s)}{F(s)} = \frac{m_2s^2 + b_2s + k} {s\big[m_1m_2s^3 + (m_2b_1 + m_1b_2)s^2 +...
  21. carb

    Mass Spring System: Modeling & Trajectory Analysis

    Hello, I'm now working on a charge limiting system. I tried modeling it an easy way to be studied. https://imageshack.us/a/img842/4572/3zvv.png A steel ball (mass "m") moves horizontaly at a continuous speed to the right. The ball has to pass over the obstacle (king of cam) which...
  22. A

    Find transfer function, model and space state of mass spring system

    The problem statement: I have to find the transfer function of a mass spring system. There are two masses in the system and 3 spring. I also have to find the state space representation and the model of the system. I have attached a image of my problem and my work so far. I think I found the...
  23. A

    Mass Spring System: Find Natural Frequencies & Mode Shapes

    Homework Statement Obtain the expressions for the natural frequencies and mode shapes for the case where m1=m2=m. Homework Equations The Attempt at a Solution I apologise for not making an attempt, this is just unlike anything I've seen. I'd appreciate if anyone could...
  24. M

    Scaling factor of a mass spring system

    Homework Statement A mass spring system carries a mass of 0.4kg. When the point of suspension is made to vibrate verticaly at a frequency of 15Hz resonance occurs. What mass should be added to the 0.4kg in order to reduce the resonant frequency to 10Hz. a) 0.20kg b) 0.40kg c) 0.50kg d)...
  25. I

    Find the maximum acceleration and accleration of a mass spring system.

    Homework Statement The problem states to find the maximum acceleration and velocity, the accleration and velocity when the displacement (x) is 1.00cm, and the equation of motion as a function of time if the displacement is A (amplitude) at t=0. We're given that the period (T) is 0.500s and...
  26. S

    Stiffness in mass spring system

    Homework Statement What happens to the frequency of oscillation if stiffness increases and why? Homework Equations ? The Attempt at a Solution Frequency increases but trying to figure out why.
  27. H

    Discuss the meaning of the result for total energy in a whole mass spring system

    Homework Statement Had to work out the total energy in a mass spring system (Part d of question), which has been found to be: (v^2*m/4)[sin^2(nt) + sin^2(3nt)] The next part of the question (e) says to 'Discuss the meaning of your result to part (d) above' And I have no idea what to...
  28. P

    Modelling A Stiff Base With A Mass Spring System

    Hi all. I am working on a problem in which I want to model the collision of a moving object, with mass m1, with a stationary base. I have calculated the velocity of the moving object at the instant of collision. I want to model this collision using a mass spring system with damping. My...
  29. Q

    Total energy of mass spring system?

    Homework Statement We have an object whose mass is 0.7 kg moves with an equation y=0.45cos8.4t. Find the general energy w=8.4 A=0.45 Homework Equations E=mv^2/2 +kA^2/2 The Attempt at a Solution So I found k using w=(k/m)^0.5. And then I found V0 using V0=A*(k/m)^0.5 and...
  30. A

    The value of spring constant in Mass spring system in an elevator

    A mass spring system is in elevator which moves upward with an acceleration "a" . What will be effect on the measured value of spring constant compared to its value when elevator is at rest. Since K= F/x At rest F=mg But with acceleration F=m(g+a) So I think the value is...
  31. F

    What went wrong with my solution for a damped mass spring system?

    So the equation is x'' + 10x' + 64x = 0 x(0) = 1 x'(0) = 0 I get general solution of e^(-5t)(c1*cos(6.245t) + c2sin(6.245t) ) From there I get e^(-5t)cos(6.245t)+5e^(-5t)sin(6.245t) but it wrong. What the gerbils am I doing wrong? Thanks
  32. K

    Damped mass spring system with with external forcing function

    Hi All, This is my first post here, and thanks in advance for any help and direction. I'm trying to model an enclosed damped mass spring system with an external forcing function acting on the system (not on the mass directly). Ultimately I would like to plot/calculate the motion (y) of...
  33. P

    Calculate Final Speeds Two Mass Spring System

    I am trying to calculate the final speeds of two masses on either side of a compressed spring, when the spring is released (in a frictionless environment). The problem has similarities to a perfectly elastic collision, in that the potential energy in the compressed spring would be the result of...
  34. X

    Mass spring system. Am I on the right track?

    Homework Statement A mass at the end of a spring with natural frequency \omega is released from rest at position x_0. The experiment is repeated byut now with the system immersed in a fluid that causes the motion to be overdamped with damping coefficient \gamma. Find the ratio of the maximum...
  35. A

    Mass Spring System: PE & KE in SHM Motion

    In a SHM motion, the PE and KE of the system is of a complement relationship. However, in a vertical mass spring system, there seem to be two kinds of PE, elastic PE in the mass spring system as well as the gravitational PE in the Earth mass system. So, what should be the PE of the SHM, and what...
  36. T

    Momentum of a mass spring system >_<

    Homework Statement Alright, so we have a .5kg mass, a .08 amplitude oscillation, and a 130 N/m spring constant (k). The question wants to know what the velocity of this mass spring will be when it is at MAX. Well, actually, it asks for the MOMENTUM of the system. The formula for that is...
  37. B

    Solving Mass Spring System with Horizontal Force Applied

    Hello PF users! This is my first post here, I'm looking for a bit of help with my mechanics assignment. 1. The question is asking me to investigate a mass with a spring and dampner attaching it to a vertical wall, and then it having a horizontal force applied to it. The mass is 0.1kg The...
  38. D

    How Do You Calculate Dynamics of a Mass Spring System?

    Homework Statement a mass spring system vibrates with an amplitude of 4.5 cm. if the spring has a constant od 250 n/m and the mass is 400 kg determine the a) total mechanical energy b) the maximum speed of the mass c) the maximum acceleration d) the speed of the mass when the displacement...
  39. A

    Calculate the total energy of the mass spring system

    Homework Statement A 12Kg mass udnergoes simple harmonic motion with an amplitude of 10cm. If the force constant for the spring is 320 N/m a) Calculate the total energy of the mass spring system. b) Calculate the maximum speed of the mass c) Calculate the speed of the mass when it is...
  40. M

    How to Solve a Three Mass Four Spring System for Transverse Vibration

    Homework Statement Three equal masses are attached to a string at equal distances from one another and from the ends, which are rasten to supports so that there is a tension T in the string. Compute normal modes and natural frequencies of small transverse vibrations about equilibrium. Describe...
  41. S

    Simple Harmonic motion with a compound mass spring system

    Homework Statement For my problem, I have two springs that have the same length, but different masses and spring constants. Both springs are secured at one end to a holder and at the other ends are connected to a single mass. My question is how do I find the angular velocity? Since the...
  42. S

    Mass spring system where springs have mass

    hello all, Recently I have been attempting to model a spring system (see below) where the springs themselves will hold mass. I should know how to do this but i accept defeat, how do you model the potential energy or a force system on two masses connected to three springs? I have read about...
  43. S

    Potential energy of mass spring system

    Ok, so the system is a ring with four identical springs connected to a single mass. Each spring is in a different quadrant and at an angle alpha from the horizontal. L is the relaxed length of each spring, k' is the spring constant, and R is the radius of the ring. and ignore gravitational and...
  44. O

    Simple Double Mass Spring System

    Homework Statement A mass m1 is held a length L above a second mass, m2, which rests on a table. There is a massless spring connecting the masses with spring constant K. You throw mass m1 upwards with velocity v0, determine the equations of position for each mass. Standard idealized conditions...
  45. Z

    Effect of mass and springs on the damping of mass spring system

    If I have mass-spring system with certain damping factor, what is the expected reduction in the damping if the mass is reduced by 25% and the spring stiffness by 50%? It is clear that the damping will decrease but how much? can anyone helps me in that?
  46. H

    Solving a 2 Mass Spring System: Forces, Equations, and Solutions"

    Homework Statement Consider two blocks of identical mass m. Block 1 can only move horizontally on a smooth table, and block 2 can only move vertically down the side of the table. Both blocks are connected by a spring (which is a direct path, so it should actually go through the table, but it...
  47. H

    How Do You Model Forces in a Two Mass Spring System?

    I would love it if someone helped me out on this problem! So, we have two identical masses. mass 1 can only move horizontally on a smooth surface, and mass two can only move vertically. These two masses are connected by a spring of constant k and the rest length of the spring is L. There is...
  48. B

    Solve Mass Spring System: Find Velocity & Compression

    A mass M is attached to the left end of a spring with a spring constant K and a mass 4M is attached to the right end. A third mass of mass M slides with velocity v and hits mass M in a completely inelastic collision. What is the velocity of the smaller mass and of the larger mass when the...
  49. R

    Max Elongation of Spring in 2 Mass Spring System

    Two blocks of masses m1 and m2 are connected by a spring of spring constant k.now forces F1 and F2 start acting on the two blocks in a manner to stretch the spring.Find the max.elongation of the spring. What I could figure out was to conserve the energy. Energy stored in spring when...
  50. G

    A mass spring system w/ recoil and Friction ?

    Homework Statement 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...