# Can anyone help me solve this DE?

• Oct 15th 2010, 11:28 AM
brittany
Can anyone help me solve this DE?
Could someone please help me solve this? I've tried and I just can't solve it. Thanks in advance for anyone who can help me!

A Particle moves along the x-axis toward the origin under the influence of a force of attraction at the origin which varies directly as the distance of the particle from the origin. At time t=0, the particle is 4 cm to the right of the origin and is moving toward the origin with a velocity of 20 cm per second and an acceleration of 64 cm per second squared.

(a) Find the position of the particle as a function of time.
(b) Find the velocity of the particle as a function of time.
(c) Find the acceleration of the particle as a function of time.
(d) Find the position of the particle at t=pi/4 seconds.

Britt
• Oct 15th 2010, 02:27 PM
zzzoak
\$\displaystyle
x''+w^2x=0
\$
Try the solution of the form
\$\displaystyle
x=Asin(wt)+Bcos(wt)
\$
Find three constants A, B, w using given initial conditions
\$\displaystyle
x(0) \; x'(0) \; x''(0)
\$