A mass of 5kg stretches a spring 10cm. The mass is acted upon by an external force of 10sin(t/2) newtons and moves in a medium that imparts a viscous force of 2N when the speed of the mass is 4cm/sec. If the mass is set in motion from its equilibrium position with an initial velocity of 3 cm/sec, formulate and solve the initial value problem describing the motion of the mass.
mx'' + γx' + kx = F0 cos(ω0t)
where γx' is the dampening force, k is the spring constant, and F0 cos(ω0t) is the external force.
The Attempt at a Solution
I know this is just a non-homogeneous second order ODE, but I am not sure where or how to get the spring constant, k, or ω. Thanks in advance for any help.