The vertical displacement y (in meters) of a lightly damped oscillator for small, dimensionless time parameter x is modeled by the infinite series
y(x)=n=0∑∞(−1)n2n+1(2x)2n+1.
Answer the questions that follow.
(a) Identify an elementary function that is equal to y(x) on its interval of convergence.
(b) Determine the largest open interval, centered at 0, for which the series representation converges.
(c) Compute y(1) in simplest exact form.
(d) Interpret the sign of y(1) in the context of the oscillator’s direction of displacement.