Error using mtimes Inner matrix dimensions must agree

hi hope anyone can help me with solving the problem. the system is

m=4.2*10^3, c=2.8*10^3, k=2*10^4, y0=0.4,

where p=sqrt((k/m)-(c^2/4m^2) and

n=c/2m

y(t)=exp(-n*t)(y0cos(pt)+y0sin(pt)(n/p));

to solve it i have done

>> m=4.2*10^3;

>> c=2.8*10^3;

>> k=2*10^4;

>> t=linspace(0,10,100);

>> p=sqrt((k/m)-((c^2)/(4*m^2)));

>> n=(c/(2*m));

>> y0=0.4;

when i use all info in the eq Y(t) it gives an error

>> y(t)=(exp(-n*t))*((y0*cos(p*t))+(y0*(n/p)*sin(p*t)));

??? Error using ==> mtimes Inner matrix dimensions must agree.

can anyone please point out my mistake and show me how to plot y(t) against t.

thanks

Answer 1

[Sean de Wolski]

You are calling * for multiplication which means it's trying to do a matrix multiply. In order to do an elementwise multiple, use .*. To help:

>>vectorize '(exp(-n*t))*((y0*cos(p*t))+(y0*(n/p)*sin(p*t)))'

     ans =
         (exp(-n.*t)).*((y0.*cos(p.*t))+(y0.*(n./p).*sin(p.*t)))

And use this as right hand side

[salman]

to find the real roots im trying fzero() function but it also gives error

x=fzero((exp(-n.*t)).*((y0.*cos(p.*t))+(y0.*(n./p).*sin(p.*t))),t)

??? Error using ==> fzero at 169 FUN must be a function, a valid string expression, or an inline function object.

Answer 2

[Matt J]

 y = vectorize(  @(t)   (exp(-n*t))*((y0*cos(p*t))+(y0*(n/p)*sin(p*t)))  );

t=linspace(...);

plot(t,y(t));