differential equation

posted by .

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.

  • differential equation -

    ML d^2è/dt^2 + k*L*dè/dt + Mg è = 0
    or

    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.

  • differential equation -

    is that true answer?

  • differential equation -

    d^2theta/dt^2 +(g/l)sin(theta)=0

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus-differential equation

    Consider the differential equation: (du/dt)=-u^2(t^3-t) a) Find the general solution to the above differential equation. (Write the answer in a form such that its numerator is 1 and its integration constant is C). u=?
  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 friction …
  3. differential equation

    A simple pendulum of length l, is oscillating through a small angle theta, in a medium for which the resistance is proportional to the velocity. Obtain the differential equation of its motion and discuss the motion
  4. Diff eqn- IVP

    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.
  5. MATH

    Differential equations, initial value problem. The general equation of motion is: mx"+Bx'+kx=f(t), where the independent variable is t, and the displacement x is the dependent variable. In this case, external force f(t)=0, so mx"+Bx'+kx=0 …
  6. Calculus

    Solve the differential equation dy/dx = -xe^y and determine the equation of the curve through P(1,2) I tried solving the differential equation and I get y = log(x^2/2 + C). Is this correct?
  7. Math

    a weight of mass m is attached to a spring and oscillates with simple harmonic motion. By Hooke's Law, the vertical displacement, y(t) satisfies the differential equation dy/dt=sqrt(k/m)*sqrt(A^2-y^2) where A(Fixed) is the maximum …
  8. Differential Equation 4

    A differential equation governing the velocity v of a falling mass m to air resistance proportional to the square of the instantaneous velocity is m dv/dt=mg-kv^2 where k>0 is a constant of proportionality. The positive direction …
  9. Physics help

    Find the differential equation of motion for a gravitational pendulum of mass m and length a by using the fact that the torque of its weight relative to the point of suspension is equal to the time derivative its angular momentum. …
  10. ordinary differential equation

    consider the differential equation d^3x/dt^3 - 9(d^2x/dt^2)+ 27(dx/dt) -27x = c0s t +sin t + te^(3t) a) show that characteristic equation of the differential equation is (m-3)^3 =0 (b) Hence, find the general solution of the equation.

More Similar Questions