Question

A mass weighing 20 N stretches a spring 6 m. The mass is initially released from rest from a point 8 m below the equilibrium position. (a) Find the position x of the mass at the times t = 7/12, 7/8, 1/6, 1/4, and 97/32 s. (Use g = 9.8 m/s2 for the acceleration due to gravity.) x(1/12) = 7.56 E * *(1/8) = 7.02 E * (1/6) = 6.29 E * x(/4) = 4.34 E * (97/32) = 3.47 E * (b) What is the velocity of the mass when t = 31/16 s? -22.8 ft/s X In which direction is the mass heading at this instant?

Answer 1

Кл: hя K ? 20 20X9.8 6 x 20 W= 1+278 Hoe Arcoste na Asin (wtto) 2 = A sin lo) &" = Aw cos (wt+6) = Aweso x= 2 sin (wt + /2) ay w(m2) = 2 sin (1.27827 + ) - 1.89 m . b) x(10) = 2 sin ( 11278 +) 1075 m

x( mla) = 2 sin (1.278. + TV) = 1.568 m . 278 * 1 tl) = 2 sin (1-278 + "%) 4 1.074 x 91T * ( 9 ) = 2 sin (1.378 290 + ) 32 32 = 0.854 by V's Bab54 2x1.278 Cas (1.27873. +62) · -1.748 m