differential equation

A simple pendulum of length is oscillating through a small angle θ in a medium for which
the resistance is proportional to the velocity. Obtain the differential equation of its motion
and discuss the motion.

  1. 👍 0
  2. 👎 0
  3. 👁 237
  1. ML d^2è/dt^2 + k*L*dè/dt + Mg è = 0

    d^2è/dt^2 + (k/M)*dè/dt + (g/L) è = 0

    k is the damping constant of proportionality (force/velocity)

    The solution is damped harmonic motion.

    1. 👍 0
    2. 👎 0
  2. is that true answer?

    1. 👍 0
    2. 👎 0
  3. d^2theta/dt^2 +(g/l)sin(theta)=0

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Pre-Calculus

    The Period T, in seconds, of a pendulum depends on the distance, L, in meters, between the pivot and the pendulum's centre of mass. If the initial swing angle is relatively small, the period is given by the radical function

  2. Physics

    A simple pendulum is made from a 0.65m long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses

  3. wcccd

    The period p of a pendulum, or the time it takes for the pendulum to make one complete swing, varies directly as the square root of the length L of the pendulum. If the period of a pendulum is 1.3 s when the length is 2 ft, find

  4. Physics

    Suppose that a simple pendulum consists of a small 66.0 g bob at the end of a cord of negligible mass. Suppose that the angle between the cord and the vertical is given by θ = (0.0800 rad) cos[(4.30 rad/s)t + ϕ] (a) What is the

  1. physics: waves

    A simple pendulum of length 1 m is released when it makes an angle of 6 degrees with the vertical. Find: a) The speed at the lowest point; b)If the mass of the bob is 260 g, what is the total energy? Thank You

  2. Physics

    A simple pendulum is oscillating with an angular amplitude 60°.If mass of bob is 50 gram the tension in the string at mean position is(g=10m/s2)

  3. momentun

    A small steel ball B is at rest on the edge of a table of height h=1m. Another steel ball A, used as the bob of a simple pendulum also of length h=1m, is released from rest with the pendulum suspension horizontal, and swings

  4. Science

    A simple pendulum oscillates with an amplitude of 30 degrees. If the length of the string is 1.0m. Calculate the velocity of the pendulum bob at its lowest point.


    In a single swing pendulum moves through an angle of 1.92 Radian. (a). Determine the length of arc treated by the pendulum Bob. (b). The area of the sector if the length of the pendulum is 13.2cm.

  2. physics

    The length of a simple pendulum is 0.79m and the mass of the particle at the end of the cable is 0.24 kg. The pendulum is pulled away from its equilibrium position by an angle of 8.5 degrees and released from rest. Assume that

  3. physics 2

    A simple pendulum is 8.00 m long. (a) What is the period of small oscillations for this pendulum if it is located in an elevator accelerating upward at 3.00 m/s2? (b) What is the period of small oscillations for this pendulum if

  4. Physic (store energy)

    Question Four A simple pendulum is used in a physics laboratory experiment to obtain an experimental value for the gravitational acceleration, g . A student measures the length of the pendulum to be 0.510 meters, displaces it 10 o

You can view more similar questions or ask a new question.