Oscillation in mechanical structures can often be described by the function:
Where t is time , ω is oscillation frequency in radians per unit time. The oscillations have a period of 2*π/ω and their amplitudes decay in time at a rate determined by τ which is called the time constant. THe smaller the value of τ the faster the oscillations die out/
a.) Use the above information to develop a criterion for choosing the spacing of t values and the upper limit on t to obtain an accurate plot of y(t). (Hint two cases: 4τ>2π/ω and 4τ<2π/ω)
b) Plot y(t) for τ= 10, ω=π and θ=2
c)Plot y(t) for τ= 0.1, ω=8π and θ=2
The Attempt at a Solution
My attempt is below, however what is bothering me is question (a). A criterion for choosing the spacing values for t and the upper limit. ?? Can't figure it out and also the hint.. How is that related? I just played around with numbers, and got those plots.