Newton's second equation of motion is ______.
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Equation of motion, mathematical formula that describes the position, velocity, or acceleration of a body relative to a given frame of reference. Newton’s second law, which states that the force F acting on a body is equal to the mass m of the body multiplied by the acceleration a of its centre of mass, F= ma, is the basic equation of motionin classical mechanics. If the force acting on a body is known as a function of time, the velocity and position of the body as functions of time can, theoretically, be derived from Newton’s equation by a process known as integration. For example, a falling body accelerates at a constant rate, g. Acceleration is the rate of change of velocity with respect to time, so that by integration the velocity v in terms of time t is given by v = gt. Velocity is the time rate of change of position S, and, consequently, integration of the velocity equation yields S = 1/2gt2.
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Equation of motion
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If the force acting on a body is specified as a function of position or velocity, the integration of Newton’s equation may be more difficult. When a body is constrained to move in a specified manner on a fixed path, it may be possible to derive the position-time equation; from this equation the velocity-time and acceleration-time equations can, theoretically, be obtained by a process known as differentiation.

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engineering; vibration
Learn how breakthroughs in motion magnification are enabling engineers to better monitor nearly imperceptible vibrations, caused by forces such as wind and rain, within buildings' infrastructures.
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Vibration, periodic back-and-forth motion of the particles of an elastic body or medium, commonly resulting when almost any physical system is displaced from its equilibrium condition and allowed to respond to the forces that tend to restore equilibrium.
Vibration
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Marin Mersenne
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Vibrations fall into two categories: free and forced. Free vibrationsoccur when the system is disturbed momentarily and then allowed to move without restraint. A classic example is provided by a weight suspended from a spring. In equilibrium, the system has minimum energy and the weight is at rest. If the weight is pulled down and released, the system will respond by vibrating vertically.
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Answer:
rate of change of momentum of an object is propotional to the applied unbalanced force in the direction of the force