Question

A 0.500 kg mass is attached to a spring of constant 150 N/m. A driving force F(t) = ( 12.0N) cos(ϝt) is applied to the mass, and the damping coefficient b is 6.00 Ns/m. What is the amplitude (in cm) of the steady-state motion if ϝ is equal to half of the natural frequency ϝ0 of the system?

Answer 1

Draw a table of your x and y values. A table of values is made by inserting different values of x into the equation and computing the results. For example, for the equation y=sin(x + ? / 2), the first two x-values (1 and 2) are: sin(1 + pi / 2) = 0.54 sin(2 + pi / 2) = -0.42.

Continue making your table of values until the numbers start to repeat. This will give you a full revolution of your wave function (a revolution will include the highest and the lowest points).

Locate the highest number in the table of values. That value will be the wave's amplitude. For the given function, y=sin(x + pi / 2), the amplitude is 1.