SIMPLE PENDULUM A simple pendulum is a particle of mass suspended from a fixed point by a m weightless, inextensible string of length It swings in a vertical plane. The forces L. acting on the particle are the gravitational force and the string tension . For small angle deviations from the vertical, the motion of the particle is approximately SHM. Applying Newton’s Second Law to the particle of mass m (8) We assume that the amplitude of the oscillation is small such that the resultant force only acts in the X direction The assumption that = 0 is only valid for small angles ( < ~15o) and the following Fy predictions do not give good agreement with measurements for large amplitude oscillations. Adding the components in the Y direction gives Adding the components in the X direction gives Therefore the acceleration in the X direction is ax (10) valid only for small values of x But the acceleration is opposite in direction to the displacement and proportional to ax x the displacement , therefore, the motion of the particle is SHM. x Equation (5) for the acceleration of a particle executing SHM is (5) Comparing equations (10) and (5), the angular frequency must be (6)
SIMPLE PENDULUM A simple pendulum is a particle of mass m suspended from a fixed point by a weightless, inextensible string of length L. It swings in a vertical plane. The forces acting on the particle are the gravitational force and the string tension . For small angle deviations from the vertical, the motion of the particle is approximately SHM. Applying Newton’s Second Law to the particle of mass m (8) We assume that the amplitude of the oscillation is small such that the resultant force only acts in the X direction The assumption that Fy = 0 is only valid for small angles ( < ~15o) and the following predictions do not give good agreement with measurements for large amplitude oscillations. Adding the components in the Y direction gives Adding the components in the X direction gives Therefore the acceleration ax in the X direction is (10) valid only for small values of x But the acceleration ax is opposite in direction to the displacement x and proportional to the displacement x , therefore, the motion of the particle is SHM. Equation (5) for the acceleration of a particle executing SHM is (5) Comparing equations (10) and (5), the angular frequency must be (6)