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Simple harmonic motion (SHM( is defined by the second order differential equation:
d2y/dt2 = -ky
where y is a fubction of time, t and is the displacement (relative to the central position), and k is a positive constant.
The equation says is that at any given position of the object undergoing SHM, its acceleration is proportional to its displacement from, and directed towards the central position.
The sine and cosine functions are solutions to the differential equation.
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Why are sine and cosine functions called harmonic?
Sinusoid shape of the sine and cosine functions appear as oscillations. If an object is moving in a straight line and its position (function of time) can be described as sinusoid then it is referred to as a simple harmonic motion.
What are the trigonometric functions?
sine, cosine, tangent, cosecant, secant and cotangent.
What are circular functions?
Sine, Cosine, Tangent, Cotangent, secant and cosecant
What is trigonometry's circular function?
The basic circular functions are sine, cosine and tangent. Then there are their reciprocals and inverses.
What are the six trigonometric functions of special angles?
sine, cosine, tangent, cosecant, secant and cotangent.
Why are sine and cosine functions called harmonic?
Sinusoid shape of the sine and cosine functions appear as oscillations. If an object is moving in a straight line and its position (function of time) can be described as sinusoid then it is referred to as a simple harmonic motion.
How do you use periodic functions in oscillation?
Many oscillations are simple harmonic motions and such motion can be represented by a sine (or equivalently, cosine) curve.
Why are sine and cosine functions used to describe periodic?
because sine & cosine functions are periodic.
How do you find the max and min of sine cosine functions?
The maximum of the sine and cosine functions is +1, and the minimum is -1.
What are the trigonometric functions?
sine, cosine, tangent, cosecant, secant and cotangent.
What are circular functions?
Sine, Cosine, Tangent, Cotangent, secant and cosecant
What is difference of using sine to cosine and tangent?
They are different trigonometric functions!
What are functions in trigonometry?
The basic functions of trigonometry are: sine cosine tangent secant cosecant cotangent
Why do you use T for period in trigonometry?
Simple harmonic motion - such as the motion of a simple pendulum, electromagnetic and other waves, tidal heights - may be modelled as sine (or cosine) curves. In these cases, the periodicity of the function is measured in units of time.
Is it possible to model everyday sounds and speech with trigonometric functions like sine cosine tangent cosecant secant or cotangent?
Yes, but only sine or cosine will suffice.
What is period as it pertains to the graph of sine and cosine?
Period is how long it takes for the sine and cosine functions to restart repeating themselves. Both have a period of 2pi (360 degrees).
Why are positive and negative numbers used on a harmonic motion graph?
Since amplitude can vary, it is inconvenient to set "0" at the maximum swing point. This can move your zero and all successive measurements with just a touch. Additionally, "simple harmonic motion" is easily described by combinations of the sine and cosine functions, and they yield positive and negative values of equal magnitudes. So it is *easier* to set zero at "mid span".
