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2. A 15 kg mass is attached to a vertical k-400 N/m spring, then pulled down and released. At some later time, the mass is 20 cm above equilibrium and moving up at 65 cm/s. If this state is t-0, then find a) the x(t) equation for the mass b) a sketch of x(t) and v(t) c) the time for the mass to reach equilibrium for the first time

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a. Equation of motion 400 Angular speed ω 5.16 radis Let Displacement be, y-Asin (ar + θ) Speed v Ao cos (ot + θ) From the given conditions. At t-0.), v-: 0.65 0.20-Asin ( 5.16 x.4cos ( θ) ) Solving it to get an(0.3076) - 17.1° 0.2938 rad 0.20 Amplitude A sin (17.109) 68 cm Equation of motiony (68 cm)sin (5.16t 0.2938)

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