The function X(t) = 8.0m cos (4pi rad/s t + pi/6 rad) At exactly 1.5 seconds, wh

Question

The function X(t) = 8.0m cos (4pi rad/s t + pi/6 rad) At exactly 1.5 seconds, what are the (a) displacement b) velocity c) acceleration d) phase of the motion e) frequency and f) period of the motion. An oscillating block - spring system has a total mechanical energy of E= 2.8 Joules, an amplitude of 2.5 cm, and a maximum speed of 1.8m/s Find: a) The spring's constant b) the mass of the block, and c) the frequency of the oscillation. A string a long which waves can travel is 2.70m long and as a mass of 260g. The tension in the string is 36N. What must be the frequency of traveling waves of amplitude 7.70 mm for the average power to be 85.0W.Two waves are described by

Explanation / Answer

Here ,

total energy , E = 2.8 J

amplitude , A = 2.5 cm = 0.025 m

maximum speed , v = 1.8 m/s

a)

let the spring constant is k

as 0.5 * k * A^2 = E

0.5 * k * 0.025^2 = 2.8

solving for k

k = 8960 N/m

the spring constant is 8960 N/m

b)

let the mass is m

as 0.5 * m * v^2 = E

0.5 * m * 1.8^2 = 2.8

m = 1.73 Kg

the mass is 1.73 Kg

c)

frequency of oscillation = 1/2pi * sqrt(k/m)

frequency of oscillation = 1/(2pi) * sqrt(8960/1.73)

frequency of oscillation = 11.5 Hz

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