Homework SourseIn an engine a piston oscillates with simpleharmonic motion
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
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
1
(b) What is its velocity?
2
(c) What is its acceleration?
3
(d) Find the period and amplitude of the motion.
4
Solution
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!
