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## Homework Statement

A particle of mass

*m*moves in one dimension under the action of a force given by

*-kx*where

*x*is the displacement of the body at time

*t*, and

*k*is a positive constant. Using

*F=ma*write down a differential equation for

*x*, and verify that its solution is

*x=Acos([tex]\omega[/tex]t+[tex]\phi[/tex])*, where [tex]\omega[/tex]

^{2}=

*k/m*(omega squared, that is). If the body starts from rest at the point

*x=A*at time

*t=0*, find an expression for

*x*at later times.

## Homework Equations

## The Attempt at a Solution

I think the differential equation they're looking for is,

*a=-kx/m*

As

*a=d*

^{2}x/dt^{2}But from here I can't see where to go; integration of course leads to the wrong formula.