1. The problem statement, all variables and given/known data An object moves with simple harmonic motion. If the amplitude and the period are both doubled, the object's maximum speed is: A) Quartered B) Halved C) Quadrupled D) Doubled E) Unchanged 2. Relevant equations x(t) = Acos(wt + [tex]\varphi[/tex]) v(t) = -wAsin(wt + [tex]\varphi[/tex]) 3. The attempt at a solution Since 2 double the period (T) is to halve the frequency (f) because of (f = 1/T), and since omega (w) = 2[tex]\pi[/tex]f...then w will be halved as well (right?): f = 1/2T --> .5f --> 2[tex]\pi[/tex].5f = .5w So that gives me: v(t) = -.5wAsin(.5w + [tex]\varphi[/tex]) And with the amplitude doubled: v(t) = -wAsin(.5w + [tex]\varphi[/tex]) Not sure if I did any of that correctly and I'm not sure what that means for my speed...is it halved? Any help would be appreciated. Thanks.