A 30.0g goldfinch lands on a slender branch, where it oscillates up and down wit

Question

A 30.0g goldfinch lands on a slender branch, where it oscillates up and down with simple harmonic motion of amplitude 3.50 X10^-2m and period 1.20 second. Part A) What is the maximum acceleration of the finch? Amax=________m/s^2 Part

B) Express your answer as a fraction of the acceleration of gravity, g. Amax/g= _____________

Part C) What is the maximum speed of the goldfinch? Vmax=_________m/s

Part D) At the time when the goldfinch experiences its maximum acceleration, is its speed a maximum or minimum?

Choices below:

1) its speed is a maximum

2) Its speed is a minimum

Explanation / Answer

Lets the Simple harmonic eqn follows

y = A*sin(t+)

v = A*cos(t+)

a = -A2*sin(t+)

T = 2/ = 1.20 => = 5.236 rad/s

A = 3.50*10-2 m

A.) Maximum acceleration when sin(t+) = -1

i.e. amax = A2 = 0.96 m/s2

B.) amax/g = 0.098

C.) Maximum speed of Goldfish

= A = 0.18 m/s

D.) Maximum acceleration when sin(t+) = -1

i.e. t+ = -/2

cos(t+) = 0

SO speed = A*cos(t+) = 0

which is minimum value of speed ( since speed can't be -ve only velocity can)

SO correct choice

2) Its speed is a minimum

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