MetroPCS LTE 8:45 PM blackboard.ncat.edu Problem 4. A 200 gram block, attached t

Question

MetroPCS LTE 8:45 PM blackboard.ncat.edu Problem 4. A 200 gram block, attached to the end of an ideal spring (horizontal) with force constant k-0 N/m, undergoes simple harmonic motion with a maximum displacement of 5.0 cm from the relaxed position. Ignore any friction or air resistance. (a) Compute the amplitude of oscillations (b) Compute the maximum speed of the block (c) At which position the velocity of the block is the maximum? ( Calculate the period of oscillations, in seconds (g) At which position the acceleration is zero? (h) At which position the velocity is zcro? (h) Calculate the frequency of the oscillations () What is the total mechanical energy of the block? x--2 x=1 2 WWA

Explanation / Answer

4.

a)

A = amplitude = maximum displacement = 5 cm

b)

w = angular frequency = sqrt(k/m) = sqrt(70/0.2) = 18.7 rad/s

Vmax = maximum speed = Aw = 0.05 x 18.7 = 0.94 m/s

c)

at x = 0 , kinetic energy is maximum, so does the speed.

d)

T = period = 2pi/w = 6.28/18.7 = 0.34 sec

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