A 175 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz
ID: 1295987 • Letter: A
Question
A 175 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x = 5.0 cm and has vx = -32 cm/s. Determine the following.
(a) the period Correct: Your answer is correct. 0.5 s
(b) the angular frequency Correct: Your answer is correct. 12.5666371 rad/s
(c) the amplitude Correct: Your answer is correct. 5.60803 cm
(d) the phase constant ??? rad
(e) the maximum speed Correct: Your answer is correct. 70.474075 cm/s
(f) the maximum acceleration ??? cm/s^2
(g) the total energy ??? J
(h) the position at t = 0.4 s ??? cm
I am stuck on D F G H, please explain in detail.
Explanation / Answer
D)x = A*cos(wt+phi)....
w = 12.56 rad/s
at t = 0s....
x = 5 cm
A = 5.60 cm
at t=0s...
x = 5.6*cos(phi)...
5 = 5.6*cos(phi)...
phi = acos(5/5.6) =0.467 rad...
F) amax = A*w^2 = 0.056*12.56*12.56 = 8.834 m/s^2
G) E = 0.5*m*w^2*A^2 = 0.5*0.175*(12.56)^2*0.056^2 =0.04328 J
H) x = 0.056*cos((12.56*0.4)+(0.467)) = 0.0393 m = 3.93 cm
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