In an engine, a piston oscillates with simpleharmonic motion so that its positio

Question

In an engine, a piston oscillates with simpleharmonic motion so that its position varies according to thefollowing expression, where x is in centimeters andt is in seconds. x =(6.00 cm) cos(t +/5) (a) At t = 0,find the position of the piston.
1

(b) What is its velocity?
2

(c) What is its acceleration?
3

(d) Find the period and amplitude of the motion.
4
x =(6.00 cm) cos(t +/5) (a) At t = 0,find the position of the piston.
1

(b) What is its velocity?
2

(c) What is its acceleration?
3

(d) Find the period and amplitude of the motion.
4

Explanation / Answer

the equation becomes x(0)=6(cos(pi/5)= 4.85 cm
b. to find velocity, take the first derivative
v= -6sin(t + pi/5) plug in t = 0 again to get v(0)= -6sin(pi/5)= -3.53 cm/sec
c. to find acceleration take the second derivative of positionor first derivative of velocity
a = -6cos(t + pi/5) a(0)= -6 cos (pi/5)= -4.85 cm/sec/sec
d. the amplitude is always the number out front.
the equation takes the form x(t) = Acos (wt + phi)
where A is the amplitude, in this case 6 cm.

Enjoy!

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