Is dfrac 1 omega omega 2
Equation for a harmonic oscillation
All vibrating systems are called Oscillators designated. Oscillators whose path-time function corresponds to a sine function are called harmonic oscillators.
What can you do with the oscillation equation?
With the oscillation equation we can calculate the deflection of a harmonic oscillator at any point in time t if the oscillation duration or frequency is known and for a known amplitude.
Depending on which of the variables ω, T or f is known, we select one of the three above-mentioned variants of the oscillation equation.
A harmonic oscillator oscillates with an oscillation period of 1.2 seconds. The maximum deflection is 12cm.
At time t = 0s the oscillator is in the rest position on the way up in the positive y-direction.
Question: Where is the oscillator at the following times
a) t = 0.6s
b) t = 1s
c) t = 1.5s?
The following values are given:
T = 1.2s
yMax = 12cm
We put into the oscillation equation for harmonic oscillations
enter the given values and calculate the respective deflection
(Danger: Calculator on WHEEL to adjust!):
a) For t = 0.6s surrendered
The Sinusterm results in 0, so the value y = 0 is also obtained for the deflection.
So the oscillator is located in the rest position. That is also logical, because the time t = 0.6s corresponds exactly to half the period of oscillation.
b) For t = 1s surrendered
The Sinusterm now gives the value -0.866. Multiplied by the amplitude of 12cm you get the value for the deflection y = -10.39cm.
The oscillator is therefore at y = -10.39cm, that is 10.39cm below the resting positionbecause in the task "above" as positive y-direction was specified.
c) For t = 1.5s surrendered
The Sinusterm results in the value 1.
The deflection therefore corresponds to the amplitude: y = yMax.
The oscillator is at the maximum deflection12cm above the rest position, so in the upper one Turning point.
The deflection can be values between yMax and -yMax accept. The sine term by which the amplitude is multiplied varies between 1 and -1.
The calculator must be set to RAD for all calculations, as the phase angle Radians is specified!
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