define simple harmonic motion.?
What is the definition of simple harmonic motion? Could you also provide some examples and explain its significance in physics?
5 Answers
In physics, simple harmonic motion (SHM) is the motion of a simple harmonic oscillator, a periodic motion that is neither driven nor damped. A body in simple harmonic motion experiences a single force which is given by Hooke's law; that is, the force is directly proportional to the displacement x and points in the opposite direction.
The motion is periodic: the body oscillates about an equilibrium position in a sinusoidal pattern. Each oscillation is identical, and thus the period, frequency, and amplitude of the motion are constant. If the equilibrium position is taken to be zero, the displacement x of the body at any time t is given by
x(t)=Acos(wt+φ)
where A is the amplitude, f is the frequency, and φ is the phase.
uncomplicated harmonic action is typified by employing the action of a mass on a spring even as that is difficulty to the linear elastic restoring stress given by employing Hooke's regulation. The action is sinusoidal in time and demonstrates a unmarried resonant frequency. study the link presented. some sensible diagrams and equations are there on your amusᴇмᴇɴt.
As much as I remember, if a particle is performing UCM, then the projection of the particle on one of the diameters of the circle performs SHM.
If you keep a candle in erect positionon a horizontal revolving table,set it in UCM and send light horizontally. The shadow of the candle on the wall performs SHM. I did this experiment so I remember it. I stopped learning Physics in 1972. Sorry if there is any error in this.
d^2x/dt^2 = -w^2.x
where w is a constant.
Alternatively you can define it in terms of the wave that is a solution to the differential equation.
x(t) = Asin(wt + k)
where A is the amplitude and k is a constant depending on the initial conditions.
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