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In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x: =, where k is a positive constant. If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic ...
In the classical sense, if f(x) ∈ C k, and g(x) ∈ C k−1, then u(t, x) ∈ C k. However, the waveforms F and G may also be generalized functions, such as the delta-function. In that case, the solution may be interpreted as an impulse that travels to the right or the left.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
for virtually any well-behaved function g of dimensionless argument φ, where ω is the angular frequency (in radians per second), and k = (k x, k y, k z) is the wave vector (in radians per meter). Although the function g can be and often is a monochromatic sine wave , it does not have to be sinusoidal, or even periodic.
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where ω is the angular frequency and k is the wavevector with magnitude | k | = k, equal to the wave number. Divide by ℏ {\displaystyle \hbar } and take the square root. This gives the relativistic frequency dispersion relation : ω ( k ) = k 2 c 2 + ( m 0 c 2 ℏ ) 2 . {\displaystyle \omega (k)={\sqrt {k^{2}c^{2}+\left({\frac {m_{0}c^{2 ...
By Krystal Hu and Kenrick Cai (Reuters) -Elon Musk's SpaceX is preparing to launch a tender offer in December to sell existing shares at a price of $135 per share, two sources familiar with the ...