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Period Of The Sum Of Two Periodic Functions

Find the period of v(t) = v_{1}(t) + v_{2}(t) if v_{1}(t) = 8sin 100πt and v_{2}(t) = 6sin 99πt and both v_{1} + v_{2} are periodic.

**The strings**:
S_{7}P_{4}A_{44} (motion - oscillatory).
**The math**:

Pj Problem of Interest is of type *motion* (motion-oscillatory).

Let T_{1} and T_{2} be the period of v_{1} and v_{2} respectively. v is periodic if its period T = n_{1}T_{1} = n_{2}T_{2}. Where n_{1} and n_{2} are integers. In other words, T is the least common integral multiple of T_{1} and T_{2}.

Now, for any periodic function asin ωt with period T, ω = 2πf. Where f is frequency in Hertz

So, f = ω/2π = 1/period = 1/T -------(1)

ω for v_{1} = 100π

So, T_{1} = 1/50

ω for v_{2} = 99π

So, T_{2} = 2/99

Now, n_{1}T_{1} = n_{2}T_{2} => n_{1}/n_{2} = T_{2}/T_{1} = (2/99)/(1/50) = 100/99.

So, n_{1} = 100 and n_{} = 99 since 100/99 is a ratio of integers in its simplest form.

So, Period of v, T = n_{1}T_{1} = n_{2}T_{2} = 100(1/50) = 99(2/99) = 2.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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