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 x = 7.00 cos(4t + pi/8) where x is in centimeters and t is in seconds. At t = 0, find the position of the piston. 6.47 cm At t = 0, find velocity of the piston. -8.036 How do you find the velocity v(t) of an object if you know the position as a function of time, x(t) At t = 0, find acceleration of the piston. -58.20 How do you find the acceleration a(t) of an object if you know the velocity as a function of time, Find the period and amplitude of the motion.

Explanation / Answer

x= 7 cos ( 4t + pi/8)

v = dx/dt = -28 sin ( 4t + pi/8)

v ( 0 ) = -28 sin ( pi/8) =-10.715 m/s

c)a= dv/dt = -112 cos ( 4t +pi/8)

a ( 0 ) =-112 cos ( pi/8) =-103.474 m/s^2

Amplitude = 7 , 2pi/ T = 4

T = pi/2 = 1.57 sec

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