I am looking for some guidance on one of my homework questions. It is as follows -
A body of the mass m is attached to a spring and moves with friction. The motion is described by the second Newton’s law
d2y/dt2 + a/m dy/dt+ k/m *y = 0,
where y is the coordinate of the body, t is the time, a > 0 is the damping coefficient, and k > 0 is the spring constant.
(a) Find the general solution of the differential equation.
(b) From your solution, how do you see that the body slows down at large times. Explain in detail. Note that values of the constants are not specified, therefore solve in general form.
Your guidance with this one is much appreciated!
A body of the mass m is attached to a spring and moves with friction. The motion is described by the second Newton’s law
d2y/dt2 + a/m dy/dt+ k/m *y = 0,
where y is the coordinate of the body, t is the time, a > 0 is the damping coefficient, and k > 0 is the spring constant.
(a) Find the general solution of the differential equation.
(b) From your solution, how do you see that the body slows down at large times. Explain in detail. Note that values of the constants are not specified, therefore solve in general form.
Your guidance with this one is much appreciated!