A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 8.50 N is applied. A 0.530-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (Assume that the direction of the initial displacement is positive.)&nbsp;(1) What is the force constant of the spring? 280 N/m&nbsp;(2) What are the angular frequency (?), the frequency, and the period of the motion?&nbsp;? = 23.121 rad/s&nbsp;f = 3.6817 Hz&nbsp;T = 0.27161 s&nbsp;(3) What is the total energy of the system? 0.35 J&nbsp;(4) What is the amplitude of the motion? 5 cm&nbsp;(5) What are the maximum velocity and the maximum acceleration of the particle?&nbsp;vmax=1.1561ms&nbsp;amax=26.73ms2&nbsp;(6) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s.&nbsp;(7) Determine the velocity and acceleration of the particle when t = 0.500 s. (Indicate the direction with the sign of your answer.)&nbsp;v = _________________&nbsp;ms&nbsp;a = _________________&nbsp;ms2

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A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 8.50 N is applied. A 0.530-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (Assume that the direction of the initial displacement is positive.)&amp;nbsp;(1) What is the force constant of the spring? 280 N/m&amp;nbsp;(2) What are the angular frequency (?), the frequency, and the period of the motion?&amp;nbsp;? = 23.121 rad/s&amp;nbsp;f = 3.6817 Hz&amp;nbsp;T = 0.27161 s&amp;nbsp;(3) What is the total energy of the system? 0.35 J&amp;nbsp;(4) What is the amplitude of the motion? 5 cm&amp;nbsp;(5) What are the maximum velocity and the maximum acceleration of the particle?&amp;nbsp;vmax=1.1561ms&amp;nbsp;amax=26.73ms2&amp;nbsp;(6) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s.&amp;nbsp;(7) Determine the velocity and acceleration of the particle when t = 0.500 s. (Indicate the direction with the sign of your answer.)&amp;nbsp;v = _________________&amp;nbsp;ms&amp;nbsp;a = _________________&amp;nbsp;ms2

nitruraviX · Accepted Answer

1)k=Fx=283.3N/m2)w=km==23.121rad/sf=w2π=3.68HzT=1f=0.2717s3)E=0.5kA2=0.354J4)5cm5)&amp;nbsp;vmax=Aw=1.1561msamax=Aw2=26.73ms26)&amp;nbsp;x=Acos⁡(wt)=5cos⁡(23.121⋅0.5)=2.677cm7)&amp;nbsp;v=−Awsin⁡(wt)=0.9765msa=−Aw2cos⁡(wt)=14.31ms21) F=kx.8.50=k(3⋅10−2)k=283.33Nm−12)&amp;nbsp;W2=kmW2=2830.530W=23.16067977rads3)&amp;nbsp;W=2πTT={W}{2π}&amp;nbsp;T=23.160679772πT=3.678812717s.Frequency&amp;nbsp;=1period=13.678812717=.272Hz4)&amp;nbsp;A=5.00cm.5)&amp;nbsp;V=−AWsin⁡Wtmax velocity is when t=1.779406359 sA=5⋅10−2mW=23.16067977V=−(5⋅10−2)(22.16067977)sin⁡(23.160679…)V=−1.02ms−1a=−AW{&amp;nbsp;2}cos⁡Wtmax acceleration is when t =0a=−AW2cos⁡Wt&amp;nbsp;

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A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 8.50 N is applied. A 0.530-kg particle rests on a frictionless h

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