Purchase Solution

Seismometer

Not what you're looking for?

Ask Custom Question

A horizontal seismometer consists of a pendulum of length "l" constrained to rotate about a nearly vertical axis. The angle away from vertical for the axis is "a" (alpha) and the mass is "m"
a. Determine the Lagrangian for the system in terms of "theta", the angular displacement away from equilibrium about the axis.
b. Find the equation of motion.
c. In the limit of small "theta" find the natural frequency of oscillation
d. If "l" is 30cm, what value of "a" (alpha) will give a period of 10 seconds?

Attached is diagram of Lehman Seismometer.

Attachments
Purchase this Solution
Solution Summary

The solution estimates Lagrangian, and also provides the equation of motion and frequency of oscillation and finally angle of inclination for given time period.

Solution Preview

Solution:
alpha (or a) == theta in the attachment,
theta == phi in the attachment
l = L in the attachment

Lagrangian, L = K - V

K = (1/2)*M*l^2 * (dQ/dt)^2 = (1/2)*M*l^2 * w^2 [ w means omega = dQ/dt]

V = M*g*l*sin(a) - M*g*l*sin(a) * cos(Q)
[Assume a tilted rod (by alpha with horizontal) rotated by theta angle. The rod tip ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
Recent Feedback
  • " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
  • "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
  • "Answer was correct"
  • "Great thanks"
  • "Perfect solution..thank you"
Purchase this Solution
Free BrainMass Quizzes
Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

The Moon

Test your knowledge of moon phases and movement.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

View More Free Quizzes
Related BrainMass Solutions

  • Explanation of the Richter Scale for Earthquakes

    According to Wikipedia, the Richter Magnitude Scale "is a base-10 logarithmic scale obtained by calculating the logarithm of the combined horizontal amplitude of the largest displacement from zero on a seismometer output."

  • Earthquakes and the Richter Scale

    "A" is the amplitude (measured in millimeters) measured directly from the photographic paper record of the Wood-Anderson seismometer, a special type of instrument.

  • Important information about Applications of Logarithmic Equations : Earthquakes and the Richter Scale

    After you measure the wave amplitude you have to take its logarithm, and scale it according to the distance of the seismometer from the earthquake, estimated by the S-P time difference. The S-P time, in seconds, makes .

  • Logarithms : Earthquakes and the Richter Scale

    The equation for Richter Magnitude is: ML = log10A(mm) + (Distance correction factor) Here A is the amplitude, in millimeters, measured directly from the photographic paper record of the Wood-Anderson seismometer, a special type of instrument.

  • Logarithmic Functions: Earthquakes and the Richter Scale

    The equation for Richter Magnitude is: ML = log10A(mm) + (Distance correction factor) Here A is the amplitude, in millimeters, measured directly from the photographic paper record of the Wood-Anderson seismometer, a special type of instrument.

  • Seismic Waves

    Both waves are detected by the seismometer. Step 2 To locate the epicenter of an earthquake there is need to examine the seismograms recorded by three different seismic stations. On each seismogram the S-P time interval is measured.

  • Logarithmic Scales

    The formula for the Richter magnitude of an earthquake is: ML = log10A(mm) + (Distance correction factor) ML is the magnitude, A is the amplitude in millimeters measured from the seismometer, and the "distance correction factor" is determined by

  • Earthquakes and the Richter Scale

    Devastating in areas several thousand miles across. 1 per 20 years The formula for the Richter magnitude of an earthquake is: ML = log10A(mm) + (Distance correction factor) ML is the magnitude, A is the amplitude in millimeters measured from the seismometer

  • Earthquakes and the Richter Scale

    Devastating in areas several thousand miles across. 1 per 20 years The formula for the Richter magnitude of an earthquake is: ML = log10A(mm) + (Distance correction factor) ML is the magnitude, A is the amplitude in millimeters measured from the seismometer

View More Related Solutions