Purchase Solution

Damping and Resonance Problem : Forces and Displacement

Not what you're looking for?

Ask Custom Question

A seismograph is a scientific instrument that is used to detect earthquakes. A simple model of a seismograph is shown below. It consists of a particle of mass m to which a pointer is attached. The particle is suspended by a spring of natural length lo and stiffness k and a damper of damping constant r from a platform of height d which is fixed to the Earth. Let the vertical displacements of the Earth, relative to a fixed origin 0, be denoted by y and let the length of the spring and the damper be x, as shown in the following diagram.

(a) Draw a force diagram showing all the forces acting on the particle.
(b) Express the forces acting on the particle in terms of the given variable and parameters.
(c) Show that the displacement x(t) of the pointer with respect to the platform satisfies the differential equation.

I think I have managed to do parts (a) and (b) successfully (but could do with a confidence check!) but had a problem with part (c):

I cannot figure out where the my: comes from on the RHS of the equation. I am taking the x origin from the top of the device and pointing downwards, which I am unsure is correct since the y origin points upwards. I can reach the equation by, when using Newton's Second Law (F=ma), I take the acceleration to be the sum of x: and y:, thus expanding to give the correct answer. But I have a feeling I am just making this up and will not gain full marks for the question ...

Attachments
Purchase this Solution
Solution Summary

Forces and displacement are investigated.

Solution Preview

Hello and thank you for posting your question to Brainmass!
The solution is ...

Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • Restoring Force, Damping Force, and Effective Spring Constant

    30185 Restoring Force, Damping Force, and Effective Spring Constant !Here's the actual problem: A) What is a restoring force? B) What is a damping force? C) What is an effective spring constant? A) What is a restoring force?

  • Driven Oscillations and Dampness

    This solution calculates the energy lost over one period using the resonance (angular frequency) and damping parameter to then find the Q of the system. All steps are shown with a brief explanation.

  • Mechanical Vibration Analysis

    The steady state solution for x(t) can be shown to be X is the displacement amplitude and f is the phase angle between displacement and force.

  • Single degree of freedom vibration problems with forcing functions

    Determine the amplitude of the steady-state displacement. Determine the critical damping coefficient, Ccr. See attached

  • underdamped parallel RLC circuit

    125407 underdamped parallel RLC circuit Problem 10.1 only. See attached file for full problem description. a) For the circuit shown above, make a plot in the complex plane that indicates the roots of the characteristic equation.

  • Differential Equation for Mechanical System

    The input is the up and down displacement of the floor and the output is the table displacement in the same direction.

  • LaPlace Transforms and Differential Equations : Masses and Springs

    Both masses are initially at rest in the equilibrium position Using Laplace transforms, derive and solve the initial value problem for the displacement function.

  • Damped Harmonic Oscillator

    (C) Determine the maximum displacement of the mass for t > 0. (D) Suppose m = 1 kg and squareroot{k/m} = 2(pi)rad/s. Calculate the maximum displacement for t > 0, as a function of v0. Hand in an accurate graph of xmax versus v0.

  • Kirchoff's Laws : Mass-Spring Equation

    What plays the role of the mass, spring constant, damping coefficient, displacement, velocity, external forcing? (b) Suppose a given circuit has no input voltage (V(t)=0) and a positive initial charge Q(0) = Qo > 0.

View More Related Solutions