(a) Please briefly describe Newton\'s three laws of motions. First law: Second l
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Question
(a) Please briefly describe Newton's three laws of motions. First law: Second lat Third law: (b) Please detenmine if the statement is TURE_or FALSE_ If the vibration is linear, the principle of superposition holds, and the mathematical techniques of analysis are well developed." (Explain periodic motion and "harmonic motion" (d) Explain 'period of vibration and "frequancy of vibration" (e) Please determine if the fumction t) illustrated on the right is a periodic function. Y N . If it is a periodic fumction, find out its: Angular frequency:-(Rad) Period: (Second) (f) For a sinusoida/function x(t) = cos(5m-1), please identify: Frequency: (Hz) period," --(Second) Initial phaseRada) (g) Read through syllabus and initial bereExplanation / Answer
(a) Newton's first law states that the state of body either rest or in motion will remain the same until an external force acts on it. For example if there were no air resistance a swinging pendulum will never stop.
Newton's second law states that rate of change of linear momentum is directly proportional to force acting on the body. F = ma is a consequence of this law.
Newton's third law states that for every action there is equal and opposite reaction. For example when you throw a ball to wall it rebounds.
(b) True because to avoid complexity we linearize the system of equations defining vibration problem so that we can apply the superposition principle.
(c) The motion which repeats itself over and over after a fixed interval of time is called periodic motion whereas harmonic motion is one in which restoring force is directly proportional to displacement. Sun revolving around a planet is an example of periodic motion and a spring system is an harmonic motion.
(d) The time interval after which same kind of motion is repeated is called period of vibrations and the number of vibrations completed in one second is called frequency of vibrations.
(e) Y ( period is 4s) angular frequency w=2f =2/t where t=4seconds. Amplitude is maximum height =2
(f) From function given angular velocity w= 5 =2f, so f=2.5 Hz period t = 1/f =1/2.5 = 0.4 second and initial phase is 1. This all is done by comparing standard equation X(t) = cos ( wt+¢) where ¢ is phase angle.
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