Answer
(a) $A = 13~cm$
(b) $x = 9.0~cm$
Work Step by Step
(a) We can find the amplitude of the oscillation as:
$v_{max} = \frac{2\pi~A}{T}$
$A = \frac{v_{max}~T}{2\pi}$
$A = \frac{(40~cm/s)(2.0~s)}{2\pi}$
$A = 12.7~cm = 13~cm$
(b) The equation for the position of the particle is:
$x(t) = A~cos(\omega~t) = A~cos(\frac{2\pi~t}{T})$
We can find the glider's position at $t = 0.25~s$ as:
$x = (12.7~cm)~cos[\frac{(2\pi)(0.25~s)}{2.0~s}]$
$x = 9.0~cm$
