How to solve an equation with multiple solutions?

[diverger]

I've a problem to solve such equations, one unknown variable, but infinite solutions, it seems mathcad only return the first one, anyone can confirm this ? And how to handle these equations in MatchCAD?

Thanks.

[ValeryOchkov]

I think you can use a numerical math for first 5-10 roots and than cos(t)=0

[diverger]

Any details? I'm new to MathCAD, can you give me one example? 5~10 roots are enough for me, thanks.

[ptc-4735478 · Accepted solution]

to find the first 5 - 10 roots first, you just have to search for the root within certain interval of x, change this interval and u find a new root. you pretty much almost have 1 solution for every half a period and less. look up root function in the mathcad help file. You can set the interval for which you are searching the solution.

and when t is large enough, the exponential function approach 0. thats why valery said the solution is just cos = 0 after couples of solution.

[diverger]

Thanks, the problem solved.

[ValeryOchkov]

You welcome:

[diverger]

The root function takes the form root(f(var), var, [a, b]). It returns the value of

var to make the function f equal to zero. The real numbers a and b are optional.

If they are specified (bracketed), root finds var on this interval. The values of a

and b must meet these requirements: a < b and f(a) and f(b) must be of opposite

signs.

It seems i must plot the two curves, then manually set the interval, or it won't give correct answer. Right ?

[AlanStevens]

Hua Zhang wrote:

It seems i must plot the two curves, then manually set the interval, or it won't give correct answer. Right ?

Not necessarily. Attached is a way of finding lots of roots in one go - at least for your given functions.

Alan