In an engine, a piston oscillates with simple harmonic motion sothat its positio

Question

In an engine, a piston oscillates with simple harmonic motion sothat its position varies according to the following expression,where x is in centimeters and t is in seconds. x = (6.00 cm)cos(3t +/6) (a) At t = 0, find the position of thepiston.
1 cm

(b) What is its velocity?
2 cm/s

(c) What is its acceleration?
3cm/s2

(d) Find the period and amplitude of the motion.
4 s
5 cm x = (6.00 cm)cos(3t +/6) (a) At t = 0, find the position of thepiston.
1 cm

(b) What is its velocity?
2 cm/s

(c) What is its acceleration?
3cm/s2

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

Explanation / Answer

Given x  = (6.00 cm)cos(3t +/6) at t = 0 , x = ( 6 cm ) cos ( / 6 )                = 5.196 cm (b). velocity v = dx / dt                      = 6 * 3 [ - sin ( 3 t + /6] so velocity at t= 0 , v = - 9 cm / s (c). accleration a = dv / dt                          = 6 * 3 * 3   [ -cos ( 3t + /6]                          = - 46.76 m / s ^ 2 (d). period T = 2 /                      =2 / 3                     = 2.094 s Amplitude A = 6 cm

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