Question

A mass m = 1 kg is attached to the end of a spring of stiffness k = 1 N / m and glides without friction on a horizontal plane. An external force F (t) = 2cos (t) is continuously applied to the mass. The mass is initially at its position of static equilibrium and its speed is zero.

mi WWW FO) X(t) 0

1.Build the problem with Initial values ​​which models this situation.

2.Calculate the displacement of the mass as a function of time.

Answer 1

män Elt) m=1kg K= 1N/m f = 2 cost According to D'Alembert poinciple mä ka= 2 cost alt) ma =f(t) F(+) ji ta = 2 cost ka Apply laplace transform » g² X (s) - 5x(0) - x'(o) + X(s) = 2 S 82 +1 & x'(o)=0 assume xlo)=o 8²X(s) + X(s) = 2s 8²41 28 X (6) - 28 (8²+1)(82+) (8²1² Since Llt sint) = 28 (8²+12 After taking inverse laplace of equation . t sint xlt)=