# when and how to use dot multiplication

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Matt Thomas on 13 May 2022
Commented: Matt Thomas on 14 May 2022
ok, for my first practice homeowrk, since i have no idea what i am doing in matlab, i was asked to plot the response of a RLC equation that is in the time domain. I got the correct answer, but im not sure what the syntax is doing and if it is needed.
q0=10;R=60;L=9;C=0.0005;
t=linspace(0,0.8)
q=q0*exp(-R*t/(2*L)).*cos(sqrt(1/(L*C)-(R/(2*L))^2)*t);
plot(t,q)
in the equation q, there is the .* operation. Is that even needed if a matrix was not even used? im confused as when to use .* vs *
a=[1 2 3]
b=[5 6 7]
a.*b
would return
5 12 21
but is .* needed in my above q equation?
thanks

Voss on 13 May 2022
"but is .* needed in my above q equation?"
Yes.
t is a vector, and q0, R, L, and C are all scalars.
q0=10;R=60;L=9;C=0.0005; % scalars
t=linspace(0,0.8); % 1-by-100 vector
Consider the expressions to the left and to the right of the .*, which both include t and some scalars:
q0*exp(-R*t/(2*L)) % vector the size of t
ans = 1×100
10.0000 9.7342 9.4755 9.2237 8.9786 8.7400 8.5077 8.2816 8.0615 7.8472 7.6387 7.4357 7.2381 7.0457 6.8584 6.6762 6.4987 6.3260 6.1579 5.9942 5.8349 5.6799 5.5289 5.3820 5.2389 5.0997 4.9642 4.8323 4.7038 4.5788
cos(sqrt(1/(L*C)-(R/(2*L))^2)*t) % vector the size of t
ans = 1×100
1.0000 0.9931 0.9726 0.9386 0.8917 0.8326 0.7620 0.6808 0.5904 0.4917 0.3864 0.2757 0.1612 0.0444 -0.0729 -0.1892 -0.3029 -0.4125 -0.5164 -0.6131 -0.7015 -0.7801 -0.8480 -0.9043 -0.9481 -0.9788 -0.9961 -0.9996 -0.9894 -0.9655
They are both vectors the size of t, so when you multiply those two vectors, you want to do it element-wise, which is what .* does
q=q0*exp(-R*t/(2*L)).*cos(sqrt(1/(L*C)-(R/(2*L))^2)*t)
q = 1×100
10.0000 9.6672 9.2155 8.6574 8.0065 7.2767 6.4825 5.6385 4.7592 3.8588 2.9513 2.0497 1.1664 0.3131 -0.5000 -1.2633 -1.9688 -2.6095 -3.1798 -3.6753 -4.0929 -4.4309 -4.6887 -4.8668 -4.9668 -4.9916 -4.9446 -4.8303 -4.6538 -4.4210
giving you another vector the size of t.
Matt Thomas on 14 May 2022
wow, thank you for all of this information. for sure helps me understand better