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 expression, x 3.00 COS 4t where x is in centimeters and t is in seconds. (a) At t 0, find the position of the piston 2.77 Cm (b) At t 0, find velocity of the piston 2.30 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 11.1 How do you find the acceleration a(t) of an object if you know the velocity as a function of time, v(t)? cm/s (d) Find the period and amplitude of the motion. period 1.57 amplitude 3.00 Cm

Explanation / Answer

b) velocity is the derivative of the position

v = 12 sin(4t+pi/8)

v = 4.59m/s at t=0

c) acceleration = derivative of velocity = -48cos(4t+pi/8)

a = 44.35 m/s2 at t=0

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