In an engine, a piston oscillates with simple harmonic motion so that its positi

Question

In an engine, a piston oscillates 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 = (3.00 cm) cos(5t + pi/7) (a) At t = 0, find the position of the piston. Your response differs from the correct answer by more than 10%. Double check your calculations, cm (b) What is its velocity? -0.02349 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully, cm/s (c) What is its acceleration? cm/s2 (d) Find the period and amplitude of the motion.

Explanation / Answer

given x = 3cm*cos(5t + pi/7)

(a)

t = 0

x = 3*(cos(pi/7))

x = 2.7 cm <<<-------answer

(b)

velocity = rate of change in position

v = dx/dt

v = -3*5*sin(5t + pi/7)

v = -15*sin(5t+ pi/7)

at t = 0

v = -15*sin((pi/7)) = -6.51 cm/s <<<<------answer

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(c)

acceleration a = rate of change in velocity

a= dv/dt

a = -3*5*5*sin(5t+pi/7)

a = -25*3*sin(5t+pi/7) = -25*x

at x = 0

a = -25*2.7 = -67.5 cm/s^2 <<<<-------answer

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(d)

period T = 2pi/w = 2*pi/5 = 1.26 s

amplitude A = 3 cm

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