the position of a mass attached to a spring is given by x = (1.5 cm) cos((3rad/s
ID: 1295814 • Letter: T
Question
the position of a mass attached to a spring is given by x = (1.5 cm) cos((3rad/s)t + pi/2)
(a) What is the amplitude of the motion
(b) What is the angular freaquency of the mass
(c) What is the period of the motion
(d) What is the maximum velocity of the mass
(e) What is the maximum acceleration of the mass
(f) What is the maximum kinetic energy of the mass
(g) What is the total energy of the mass
(h) What is the maximum potential energy of the mass
(i) What is the kinetic energy of the mass at x = 1.0 cm
(j) What is the kinetic energy of the mass at t = 1.0 s
Explanation / Answer
x = (1.5 cm) cos((3rad/s)t + pi/2)
a)
amplitude = 1.5 cm
b)
ang frequency , w = 3 rad/s
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c)
period T = 2pi/w = 6.28/3 = 2.09 sec
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d)
maximum velocity , V = wA = 3*1.5 = 4.5 cm/s
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e)
maximum accleration = w^2*A = 9*1.5 = 13.5 cm/s^2
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f)
macimum kinetic energy = 0.5mv^2 = 0.5*m*(0.045)^2 J
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g)
total energy = 0.5*m*(0.045)^2 J
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h)
velocity at x = 1 cm
v = w*sqrt(A^2-x^2) = 3*sqrt(1.5^2-1^2)
K = 0.5mv^2
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j)
Kintic energy at t = 1 s
K =0.5 mv^2
mass is needed for f - j
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