Solving a Harmonic Motion Problem: Finding Position, Velocity, and Acceleration

[chocolatelover]

Hi everyone,

Could someone please help me with this problem?

Homework Statement

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

Homework Equations

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

 

[rock.freak667]

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

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

 

[chocolatelover]

Thank you very much

Regards