#include <stdio.h>
 
void test( float dt, int steps )
{
    float x = 100.0f;
	float v = 0;
	for ( int i = 0; i < steps; i++ )
	{
	        v = v - .1f * x * dt;
        	x = x + v * dt;
	}
        printf("%g\n", x);
};
 
int main(int argc, char **argv) {
 
    test( 1, 20 );
    test( 0.1, 200 );
    test( 0.01, 2000 );
    test( 1, 40 );
    test( 0.1, 400 );
    test( 0.01, 4000 );
    test( 1, 80 );
    test( 0.1, 800 );
    test( 0.01, 8000 );
    return 0;
}

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