Question

A vertical spring has a spring constant 50 N/m. At t = 0 a force given in newtons by F (t) = 48 cos 7t, t ≥ 0 is applied to a 20 N weight which hangs in equilibrium at the end of the spring. Neglecting damping find the position of the weight at any later time t.

Answer 1

We have the equation of motion

The graph of x vs. t is shown by the heavy curve of Fig. 4.6. The dashed curves are the curves of x = + 2 sin t. If we consider that 2 sin t is the amplitude of sin 6t, we see that the amplitude varies sinusoidally. The phenomenon is known as amplitude modulation (see problem 14 chapter 2).