The balance wheel of a watch vibrates with an angular amplitude 0, angular frequ

Question

The balance wheel of a watch vibrates with an angular amplitude 0, angular frequency , and phase angle =0

Part A

Find an expression for the angular velocity d/dt as a function of time.

Express your answer in terms of the given quantities.

Part B

Find an expression for the angular acceleration d2/dt2 as a function of time.

Express your answer in terms of the given quantities.

Part C

Find the balance wheel's angular velocity when its angular displacement is 0.

Express your answer in terms of the given quantities.

Part D

Find the balance wheel's angular velocity when its angular displacement is 0/2 and is decreasing.

Express your answer in terms of the given quantities.

Part E

Find the balance wheel's angular acceleration when its angular displacement is 0/2 and is decreasing.

Express your answer in terms of the given quantities.

Explanation / Answer

angular displacement @ = @0 cos(wt + phi )

@ =@0 cos(wt)

a) angular velocity = d@ / dt = (@0 * w) (- sinwt)

              = - @0w sin(wt)

b) angular acceleration= d^2 @ / dt^2 = d (- @0w sin(wt) ) / dt

      = - @0 w^2 cos(wt)

c) when @ = 0

thet means wt = pi /2

angular velocity = - @0 w sin(pi/2) = @0 *w

D) @0 /2 = @0 cos(wt)

wt = 2 pi / 3

angular velocity = @0 *w sin(2pi/3) = 0.866*@0@w

e) angular accc. = Q0 w^2 cos(2pi /3) = @0 * w^2 /2

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