Period Of The Sum Of Two Periodic Functions
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Period Of The Sum Of Two Periodic Functions

Find the period of v(t) = v1(t) + v2(t) if v1(t) = 8sin 100πt and v2(t) = 6sin 99πt and both v1 + v2 are periodic.

The strings: S7P4A44 (motion - oscillatory).

The math:
Pj Problem of Interest is of type motion (motion-oscillatory).

Let T1 and T2 be the period of v1 and v2 respectively. v is periodic if its period T = n1T1 = n2T2. Where n1 and n2 are integers. In other words, T is the least common integral multiple of T1 and T2.

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 v1 = 100π
So, T1 = 1/50
ω for v2 = 99π
So, T2 = 2/99

Now, n1T1 = n2T2 => n1/n2 = T2/T1 = (2/99)/(1/50) = 100/99.
So, n1 = 100 and n = 99 since 100/99 is a ratio of integers in its simplest form.
So, Period of v, T = n1T1 = n2T2 = 100(1/50) = 99(2/99) = 2.

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