The harmonic motion amplitudes (unlike the RAO responses of the vessel) are not relative to a wave amplitude – they are given directly in length units (for surge, sway and heave) or degrees (for roll, pitch and yaw). If you are modelling slow drift, the amplitudes for heave, roll and pitch will usually be set to zero. the amplitude and phase lag of the motion for each of the 6 degrees of freedom of the vessel.the period of the harmonic motion this applies to all 6 degrees of freedom,.These harmonic motions are in addition to any wave-generated motion resulting from the RAO data, so if you only want the wave-generated motion then you should set the number of harmonic motions to zero.Įach harmonic motion is a single-period sinusoidal motion of the vessel, defined by The simplest oscillations occur when the restoring force is directly proportional to displacement.The harmonic motion data apply if the vessel's superimposed motion is RAOs + harmonics, allowing you to define a number of harmonic motions of the vessel. From there, the motion will repeat itself. (e) In the absence of damping (caused by frictional forces), the ruler reaches its original position. (d) Now the ruler has momentum to the left. It stops the ruler and moves it back toward equilibrium again. (c) The restoring force is in the opposite direction. (b) The net force is zero at the equilibrium position, but the ruler has momentum and continues to move to the right. Restoring force, momentum, and equilibrium: (a) The plastic ruler has been released, and the restoring force is returning the ruler to its equilibrium position. These forces remove mechanical energy from the system, gradually reducing the motion until the ruler comes to rest. It is then forced to the left, back through equilibrium, and the process is repeated until dissipative forces (e.g., friction) dampen the motion. However, by the time the ruler gets there, it gains momentum and continues to move to the right, producing the opposite deformation. Once released, the restoring force causes the ruler to move back toward its stable equilibrium position, where the net force on it is zero. The deformation of the ruler creates a force in the opposite direction, known as a restoring force. When the ruler is on the left, there is a force to the right, and vice versa.Ĭonsider, for example, plucking a plastic ruler shown in the first figure. Oscillating Ruler: When displaced from its vertical equilibrium position, this plastic ruler oscillates back and forth because of the restoring force opposing displacement. It is common convention to define the origin of our coordinate system so that x equals zero at equilibrium. This is the equilibrium point, where the object would stay at rest if it was released at rest. In one dimension, we can represent the direction of the force using a positive or negative sign, and since the force changes from positive to negative there must be a point in the middle where the force is zero. If an object is vibrating to the right and left, then it must have a leftward force on it when it is on the right side, and a rightward force when it is on the left side.
It is important to understand how the force on the object depends on the object’s position. Without force, the object would move in a straight line at a constant speed rather than oscillate. Newton’s first law implies that an object oscillating back and forth is experiencing forces. If you calibrate your intuition so that you expect large frequencies to be paired with short periods, and vice versa, you may avoid some embarrassing mistakes on physics exams. The horizontal axis represents time.įor example, if a newborn baby’s heart beats at a frequency of 120 times a minute, its period (the interval between beats) is half a second. Sinusoidal Waves of Varying Frequencies: Sinusoidal waves of various frequencies the bottom waves have higher frequencies than those above. Note that period and frequency are reciprocals of each other. Frequency is usually denoted by a Latin letter f or by a Greek letter ν (nu). The frequency is defined as the number of cycles per unit time.
) One complete repetition of the motion is called a cycle. (The symbol P is not used because of the possible confusion with momentum. The usual physics terminology for motion that repeats itself over and over is periodic motion, and the time required for one repetition is called the period, often expressed as the letter T.
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