What is the difference between simple and physical pendulum

A pendulum consists of an object suspended along an axis so that it is able to move back and forth freely. Depending on the shape of the pendulum, a pendulum could be classified as a simple pendulum or a compound pendulum physical pendulum. There is no clear-cut definition to differentiate between a simple pendulum and a compound pendulum, however, so this is a rather qualitative distinction. As mentioned earlier, in a simple pendulum the dimensions of the object in suspension is significantly smaller than the distance from the centre of gravity of the object to the axis of suspension.

This allows us to treat the mass as though it were a single point. The figure below illustrates a simple pendulum:. Then, if we let the bob to oscillate back-and-forth with a small angle , then we can show that the body will oscillate with a period given by:.

Any object can oscillate like a pendulum. Consider a coffee mug hanging on a hook in the pantry. If the mug gets knocked, it oscillates back and forth like a pendulum until the oscillations die out. We have described a simple pendulum as a point mass and a string.

A physical pendulum is any object whose oscillations are similar to those of the simple pendulum, but cannot be modeled as a point mass on a string, and the mass distribution must be included into the equation of motion. As for the simple pendulum, the restoring force of the physical pendulum is the force of gravity. With the simple pendulum, the force of gravity acts on the center of the pendulum bob.

In the case of the physical pendulum, the force of gravity acts on the center of mass CM of an object. The object oscillates about a point O. Consider an object of a generic shape as shown in Figure. Taking the counterclockwise direction to be positive, the component of the gravitational force that acts tangent to the motion is.

The minus sign is the result of the restoring force acting in the opposite direction of the increasing angle. Recall that the torque is equal to. The magnitude of the torque is equal to the length of the radius arm times the tangential component of the force applied,.

Here, the length L of the radius arm is the distance between the point of rotation and the CM. To analyze the motion, start with the net torque. Like the simple pendulum, consider only small angles so that. Recall from Fixed-Axis Rotation on rotation that the net torque is equal to the moment of inertia. Once again, the equation says that the second time derivative of the position in this case, the angle equals minus a constant.

In extreme conditions, skyscrapers can sway up to two meters with a frequency of up to Several companies have developed physical pendulums that are placed on the top of the skyscrapers. As the skyscraper sways to the right, the pendulum swings to the left, reducing the sway. Assuming the oscillations have a frequency of 0. What should be the length of the beam?

We are asked to find the length of the physical pendulum with a known mass. We first need to find the moment of inertia of the beam. We can then use the equation for the period of a physical pendulum to find the length.

There are many ways to reduce the oscillations, including modifying the shape of the skyscrapers, using multiple physical pendulums, and using tuned-mass dampers. A torsional pendulum consists of a rigid body suspended by a light wire or spring Figure. When the body is twisted some small maximum angle. The restoring torque can be modeled as being proportional to the angle:. The minus sign shows that the restoring torque acts in the opposite direction to increasing angular displacement.

The net torque is equal to the moment of inertia times the angular acceleration:. This equation says that the second time derivative of the position in this case, the angle equals a negative constant times the position.

This looks very similar to the equation of motion for the SHM. A string is attached to the CM of the rod and the system is hung from the ceiling Figure. The rod is displaced 10 degrees from the equilibrium position and released from rest. The rod oscillates with a period of 0. What is the torsion constant. We are asked to find the torsion constant of the string. We first need to find the moment of inertia. Like the force constant of the system of a block and a spring, the larger the torsion constant, the shorter the period.

The period of a physical pendulum. The length between the point of rotation and the center of mass is L. The object oscillates about a point O. The minus sign is the result of the restoring force acting in the opposite direction of the increasing angle.

Here, the length L of the radius arm is the distance between the point of rotation and the CM. To analyze the motion, start with the net torque. The solution is. In extreme conditions, skyscrapers can sway up to two meters with a frequency of up to Several companies have developed physical pendulums that are placed on the top of the skyscrapers.

As the skyscraper sways to the right, the pendulum swings to the left, reducing the sway. Assuming the oscillations have a frequency of 0. What should be the length of the beam? We are asked to find the length of the physical pendulum with a known mass. We first need to find the moment of inertia of the beam. We can then use the equation for the period of a physical pendulum to find the length. There are many ways to reduce the oscillations, including modifying the shape of the skyscrapers, using multiple physical pendulums, and using tuned-mass dampers.

The restoring torque is supplied by the shearing of the string or wire. The minus sign shows that the restoring torque acts in the opposite direction to increasing angular displacement. The net torque is equal to the moment of inertia times the angular acceleration:. This equation says that the second time derivative of the position in this case, the angle equals a negative constant times the position. Therefore, the period of the torsional pendulum can be found using.

The rod oscillates with a period of 0. We are asked to find the torsion constant of the string. We first need to find the moment of inertia.