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APUGYael
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I divide by zero which is a no-go, but on the other hand: at resonance frequency the phase-shift is 90 degrees.
BvU said:Yes, at ##\omega_u = \omega_0## you have ##\cos\phi = 0 ##. You don't actually divide by 0, it's just that the tangent of ##\phi## is undetermined.
BvU said:I missed that question.
The answer is: no. The denominator is zero, the numerator doesn't have to be 1, just non-zero.
##D## is a free parameter, like ##C## and ##J##.
Not with x = pi/2 but via the limit x-> pi/2.APUGYael said:But surely
tan (x) = sin(x)/cos(x) with x = pi/2 means that
sin(pi/2)=1
A.T. said:Not with x = pi/2 but via the limit x-> pi/2.
It shows in a drastic way that it's a bad habit to use the tan function to calculate polar angles in polar coordinates (and this example of the phase shift is geometrically interpreted right this). What you really want is to calculate an angle within an interval of the length ##2 \pi## not one of the length ##\pi##.BvU said:Yes, at ##\omega_u = \omega_0## you have ##\cos\phi = 0 ##. You don't actually divide by 0, it's just that the tangent of ##\phi## is undetermined.
Harmonic oscillation is a type of motion in which an object moves back and forth between two points, with the motion repeating itself in a regular pattern.
Harmonic oscillation is caused by a restoring force, which is a force that acts to bring the object back to its equilibrium position after it has been displaced.
Some examples of harmonic oscillation include a pendulum swinging back and forth, a mass on a spring moving up and down, and a guitar string vibrating.
Harmonic oscillation is typically measured by the frequency, which is the number of complete oscillations per unit of time, and the amplitude, which is the maximum displacement of the object from its equilibrium position.
Harmonic oscillation has many practical applications, such as in timekeeping devices like clocks and watches, musical instruments, and even in the design of buildings and bridges to withstand vibrations caused by earthquakes or wind.