Question

1. An oscillator of mass 2 Kg has a damping constant of 12 kg/sec and a spring constant of 10N/m. What is its complementary position solution? If it is subject to a forcing function of F(t)= 2*sin(2t) what is the equation for the position with respect to time? Equation 2(x2) + 12(x1) + 10(x) = 2*sin(2t); x2 is the 2nd derivative of x; x1 is the 1st derivative of x.

Answer 1

Force equation is,

so by putting values and for C.F solution we can write it from fourier technique as

solving this quadratic equation we get

so,

m=-1 and -5

so,C.F

now external force if acts then we can write

solving for Prticular integral we write

so using property for sin(mx)

now using upto first order

so final solution is,

so,