# Simple Harmonic Motion and acceleration

1. Dec 14, 2009

### hodgepodge

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
x(t) = A cos (omega*(t) + phi)

3. 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, doesnt 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

2. Dec 14, 2009

### jdwood983

Well you are given a position,

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

and how do you get a velocity, $v(t)$, from a position? Similarly, how do you get an acceleration, $a(t)$, from a velocity?

3. Dec 14, 2009

### hodgepodge

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

4. Dec 14, 2009

### jdwood983

Correct. After taking the derivatives, just put in for $t=1$ 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):

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

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

5. Dec 14, 2009

### hodgepodge

Thank you so much.