Simple Harmonic Motion, velocity and acceleration

[hodgepodge]

Homework Statement

a body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x=5.0 sin (pi*(t) + pi/3). What is the velocity in m/s and acceleration in m/s^2 of the body at t=1.0s?

Homework Equations

x(t) = A cos (omega*(t) + phi)

The Attempt at a Solution

i am just confused as to how the equation in the problem is sin, vs. cos in the relevant equation, doesn't this just mean that the period of the motion of the object starts at a different point and can i use pi*(t) to find omega*(t) and pi/3 to find phi and get my velocity and accelerations, or do i have to manipulate the equation in the problem to get it in the form in relevant equations...if so what would i do to get the sin into cos?

thanks

 

[jdwood983]

Well you are given a position,

[tex]
x(t)=5.0\sin\left[\pi t+\frac{\pi}{3}\right]
[/tex]

and how do you get a velocity, [itex]v(t)[/itex], from a position? Similarly, how do you get an acceleration, [itex]a(t)[/itex], from a velocity?

 

[hodgepodge]

so i could just take the derivative and find instantaneous velocity and then take second derivative for instantaneous acceleration?

 

[jdwood983]

Correct. After taking the derivatives, just put in for [itex]t=1[/itex] and you'll have your velocity and accelerations at the appropriate time.


Also, since I didn't quite answer Part 3 very well, to get cosine from sine (and vice versa):

[tex]
\sin[\theta]=\cos\left[\frac{\pi}{2}-\theta\right]
[/tex]

[tex]
\cos[\theta]=\sin\left[\frac{\pi}{2}-\theta\right]
[/tex]

 

[hodgepodge]

Thank you so much.