Maxima/Root Mean Square (RMS)

Root Mean Square (RMS) with Maxima

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Main_Page > Maxima > Root Mean Square (RMS) with Maxima

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Root Mean Square (RMS) Calculation

v(Vm,t):= Vm*sin(ω*t+φ);

Vrms(Vm) := sqrt(integrate(1/T*v(Vm,t)^2,t,t0,t0+T));

(%o1)	v(Vm,t):=Vm*sin(ω*t+φ)
(%o2)	Vrms(Vm):=sqrt(integrate(1/T*v(Vm,t)^2,t,t0,t0+T))

${\sqrt {{\frac {1}{T}}\int \limits _{t_{0}}^{{t_{0}}+T}Vm^{2}\sin(\omega t+\phi )^{2}\,dx}}$

f : 60 $ /* Frequency (Hz) */
Vm : 169.7056274847714 $  /* Input Voltage (V) */;
T : 1/f $ /* Period (s) */
t0 : 0 $ /* Initial time (s) */
ω: 2*π*60 $ /* Angular Velocity (rad/s) */
φ : 0 $ /* initial time (s) */

Vrms(Vm);
120.0

plot2d([v(Vm,t), Vrms(Vm), -Vrms(Vm)], [t,0,2*T]);