Not what you're looking for?
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 ...
Purchase this Solution
Forces and displacement are investigated.
Hello and thank you for posting your question to Brainmass!
The solution is ...
Purchase this Solution
Free BrainMass Quizzes
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.
This quiz test you on how well you are familiar with solving quadratic inequalities.
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Some questions on probability