In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, X = 6.00 cos (3t + where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. 5.196 cm (b) At t = 0, find velocity of the piston. -5 How do you find the velocity v(t) of an object if you know the position as a function of time, x(t)? cm/s (c) At t = 0, find acceleration of the piston. -17.3 How do you find the acceleration a(t) of an object if you know the velocity as a function of time, v(t)? cm/s2 (d) Find the period and amplitude of the motion. period 2.09 amplitude 6 cm

Physics for Scientists and Engineers: Foundations and Connections
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Author:Katz, Debora M.
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In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression,
X = 6.00 cos ( 3t +
where x is in centimeters and t is in seconds.
(a) At t = 0, find the position of the piston.
5.196
cm
(b) At t = 0, find velocity of the piston.
-5
How do you find the velocity v(t) of an object if you know the position as a function of time, x(t)? cm/s
(c) At t = 0, find acceleration of the piston.
-17.3
How do you find the acceleration a(t) of an object if you know the velocity as a function of time, v(t)? cm/s2
(d) Find the period and amplitude of the motion.
period
2.09
S
amplitude 6
cm
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Transcribed Image Text:In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, X = 6.00 cos ( 3t + where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. 5.196 cm (b) At t = 0, find velocity of the piston. -5 How do you find the velocity v(t) of an object if you know the position as a function of time, x(t)? cm/s (c) At t = 0, find acceleration of the piston. -17.3 How do you find the acceleration a(t) of an object if you know the velocity as a function of time, v(t)? cm/s2 (d) Find the period and amplitude of the motion. period 2.09 S amplitude 6 cm Need Help? Read It Watch It
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