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. Solve this equation to obtain the equation of motion in the small oscillation approximation, by considering that initially the pendulum at rest makes an angle è0 with the Oy axis (vertical).

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A simple pendulum suspended in a rocket ship has a period To. Assume that the rocket ship is near the earth in a uniform gravitational field. Determine for each of the following statements whether it is correct or incorrect. If

  2. 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

  3. Differential Equations

    The velocity v of a freefalling skydiver is well modeled by the differential equation m*dv/dt=mg-kv^2 where m is the mass of the skydiver, g is the gravitational constant, and k is the drag coefficient determined by the position

  4. Physics

    A simple pendulum of length 2.00m is made with a mass of 2.00kg. The mass has speed of 3.00 m/s when the pendulum is 30 degrees above its lowest position. -What is the maximum angle away from the lowest position the pendulum will

  1. Physics Help please

    The free-fall acceleration on Mars is 3.7 m/s2. (a) What length pendulum has a period of 4 s on the earth? cm What length pendulum would have a 4 s period on Mars? cm (b) A mass is suspended from a spring with force constant 10

  2. physics

    A ball of mass 0.075 kg is fired horizontally into a ballistic pendulum. The pendulum mass is 0.350 kg. The ball is caught in the pendulum, and the centerof mass of the system rises a vertical distance of 0.145 m in the earth's

  3. Physics

    In a ballistic pendulum experiment, a small marble is fired into a cup attached to the end of a pendulum. If the mass of the marble is 0.0255 kg and the mass of the pendulum is 0.250 kg, how high will the pendulum swing if the

  4. calculus

    Question 1: Experimentally it is found that a 6 kg weight stretches a certain spring 6 cm. If the weight is pulled 4 cm below the equilibrium position and released: a. Set up the differential equation and associated conditions

  1. Algebra 2

    Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of the pendulum has an arc length of 100cm

  2. Calculus application of sin function

    a horizontal position of the pendulum of a grandfather clock can be modelled by h(t)=Acos(2(pi)t/T), where A is amplitude of the pendulum in meters, t is time in seconds, and T is the period of the pendulum, in seconds. If the

  3. Physics

    A bob of mass m is suspended from a string of length L, forming a pendulum. The period of this pendulum is 1.97 s. If the pendulum bob is replaced with one of mass 1/2 m and the length of the pendulum is increased to 2.50 L, what

  4. Physics

    A particle with a mass of 0.660 kg is attached to a horizontal spring with a force constant of 23.76 N/m. At the moment t = 0, the particle has its maximum speed of 15 m/s and is moving to the left. (Assume that the positive

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