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**1. Homework Statement**

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. Homework 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.