# Harmonic motion problem

1. May 5, 2008

### chocolatelover

Hi everyone,

1. The problem statement, all variables and given/known data
In an engine, a piston oscilates with simple harmonic motion so that its position varies according to the following expression, where x is in centimeters and t is in seconds.
x=5.00cmcos(3t+pi/5)

a. At t=0, find the position of the piston
b. What is its velocity?
c. What is its acceleration?
d. Find the period and amplitude of the motion

2. Relevant equations

3. The attempt at a solution

a. 5cmcos(3(0)+pi/5)=5cos(pi/5)=4.05cm

b. -5sin(pi/5)=-2.9

c. -5cos(pi/5)=-4.05

d. 5cm=amplitude

Thank you very much

2. May 5, 2008

### rock.freak667

$x=5cos(3t+\frac{\pi}{5})$

$$v=\frac{dx}{dt}=-5sin(3t+\frac{\pi}{5}) \times 3=-15sin(3t+\frac{\pi}{5})$$

3. May 5, 2008

### chocolatelover

Thank you very much

Regards