Consider an object that is attached to a horizontally oscillating piston. The ob

Question

Consider an object that is attached to a horizontally oscillating piston. The object moves with a velocity given by v = B sin(wt), where B and w (lower case Greek omega) are constants and w is in s-1.

(a) Explain why B is equal to the maximum speed vmax.

(b) Determine the acceleration of the object as a function of time. (Use the following as necessary: w, vmax, and t.)

a =  

Is the acceleration constant?

(c) What is the maximum acceleration (magnitude) in terms of w and vmax.

|amax| =

(d) At t = 0, the object's position is known to be x0. Determine the position as a function of time in terms of t, w, x0 and vmax.

x =

Explanation / Answer

a) vmax = B x max of(sin(wt))

max of sinwt =1

v_max = B

b) a = dv/dt = Bwcos(wt)

c) a_max = Bw x max of(cos(wt))

max of coswt =1

a_max = Bw

d) dx/dt = v = Bsin(wt)

x = x0 - Bcos(wt)/w

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