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=(4.00cm)cos(3t+π/6)(a) At t=0, find the position of the piston.(b) What is its velocity?(c) What is its acceleration?(d) Find the period and amplitude of the motion.

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09-12-2022
Physics

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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=(4.00cm)cos(3t+π/6)(a) At t=0, find the position of the piston.(b) What is its velocity?(c) What is its acceleration?(d) Find the period and amplitude of the motion.

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kumarprabhat kumarprabhat · Answer 1 · 2022-12-17T10:11:00-05:00

A) 3.99 cm, B)-7.99 cm/s, C)-15 cm/s2, D) 4 cm, In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the following expression,

a) At t=0

x=4.00cm)cos(3t+π/6)(a)= 4*0.999 = 3.999 cm

b)Expression for velocity v = dx/dt = -8.00 Sin(3t+π/6)

At t=0 v= -8 Sin(π/6) = -7.999 cm/s

c) Expression for acceleration a= -16 Cos(3t+ π/6)

At t=0 a= -16 Cos(π/6) = -15.99 cm/ sec2

d) Period = (2 ?)/3

Amplitude= 4 cm

A piston is a part of a variety of comparable devices, including reciprocating engines, reciprocating pumps, gas compressors, hydraulic cylinders, and pneumatic cylinders.

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