5. Aparticle moving along the x-axis in simple harmonic motionstarts from it\'s

Question

5. Aparticle moving along the x-axis in simple harmonic motionstarts from it's equillibrium position, the origin, at t = 0and moves to the right. The amplitude of it's motion is 2cm, andthe frequency is 1.5Hz. b.)Find the earliest time (t > 0) at which the paricleexperiences it's maximum speed. c.) Find the earliest time (t > 0) at which the particlehas it's maximum acceleration. d.) Find the total distance travelled between t = 0 and t =1s. 5. Aparticle moving along the x-axis in simple harmonic motionstarts from it's equillibrium position, the origin, at t = 0and moves to the right. The amplitude of it's motion is 2cm, andthe frequency is 1.5Hz. b.)Find the earliest time (t > 0) at which the paricleexperiences it's maximum speed. c.) Find the earliest time (t > 0) at which the particlehas it's maximum acceleration. d.) Find the total distance travelled between t = 0 and t =1s.

Explanation / Answer

A = .02m     f = 1.5Hz
b.) The particle will have maximum velocity at equilibrium,when Kinetic Energy is highest. this will be at 1/2of the period. t = .5(1/1.5) ˜ .3 seconds c.) the maximum acceleration will occur at theamplitude. This will be 1/4 of the period.       t = .25(1/1.5) ˜ .167seconds d.) The formula for position of an oscillating particle at anytime is:       x =Acos(2ft)       x =.02cos(2(1.5)1)      x ˜.0197

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