#HARMONIC MOTION SERIES#
#HARMONIC MOTION FREE#

Mass attached to two vertical springs connected in parallel Mass attached to two vertical springs connected in series Simple pendulum Liquid oscillating in a U-tube Applications of s.h. Therefore acceleration a of the system is given by a = -(k/m)x.(5)Įquation (5) clearly shows that an oscillating spring mass system in the vertical exhibits simple harmonic motion since its equation of motion is of the form of the fundamental equation of simple harmonic motion. Harmonic motion can mean: the displacement of the particle executing oscillatory motion that can be expressed in terms of sine or cosine functions known as harmonic motion. Negative sign shows the the restoring force and the displacement x increase in opposite directions. Where a is the acceleration of the system upwards. Now there are many objects that behave like swings in their motion (In classical physics this behavior is termed SIMPLE HARMONIC MOTION). Restoring force on the mass is given by T' - mg = -ma.(3) This means that the time taken for one complete cycle is the same. Suppose the mass is displaced downwards by an amount x and then released.The new tension T' is now given by In simple harmonic motion, the frequency and time period are independent of the amplitude. A periodic vibration, as of a pendulum, in which the motions are symmetrical about a region of equilibrium. The deformation of the ruler creates a force in the opposite direction, known as a restoring force. Consider, for example, plucking a plastic ruler to the left as shown in Figure 5.38. Simple harmonic motion (SHM) is oscillatory motion for a system where the restoring force is proportional to the displacement and acts in the direction opposite to the displacement. Hence, these are two motions that have opposite results. Without force, the object would move in a straight line at a constant speed rather than oscillate. Damped oscillation is similar to forced oscillation except that it has continuous and repeated force. Show how the amplitude decreases with time.

#HARMONIC MOTION FREE#

Attach a mass to the free end, and add a damping card. Alternatively, clamp a springy metal blade (e.g.

Where g is the acceleration due to gravity.įrom Hooke's law, T = ke where k is the spring constant and e is the extension produced in the spring by the mass m. An object or a system is oscillating in its own natural frequency without the interference of an external periodic force or initial motion. Set up a suspended mass-spring system with a damper a piece of card attached horizontally to the mass to increase the air drag. where xm is the amplitude of the oscillation, and is the phase constant of the oscillation. The tension T in the spring is equal to the weight mg of the body.