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## Homework Statement

A 1 kg mass is attached to a spring with constant k = 16 N/m. Find the motion x(t) in amplitude-phase form (2.37) if x(0) = 1 and x′(0) = −1.

Ignore damping forces.

## Homework Equations

combined with 3

## The Attempt at a Solution

So I know m=1, k=16, c=0, x0=1, and v0=-1

w=sqrt(k/m)=sqrt(16)=4

md^2x/dt^2+kx=0

characteristic equation

mr^2+k=0

r=+/-iw=+/-4i

x(t)=c1*cos(4t)+c2*sin(4t) (e^0t = 1 and is excluded)

initially x0=1 so

1=c1

v=x'=-4c1sin(4t)+4c2cos(4t)

use intial value of -1 for v

-1=4c2cos(0)=4c2

c2=-1/4

A=sqrt(c1^2+c2^2)=sqrt(17)/4

tan(phi)=c2/c1=-.245, add pi =2.90

so now we have

x(t)=Acos(wt-phi)=sqrt(17)/2*cos(4t-2.90)

the book says the answer should be sqrt(17)/16*cos(4t-6.038)

so I all have right is the angular frequency

where did I mess up?