Question

A 3.50 kg mass is attached to a spring and set into motion horizontally along a frictionless track. At time t = 0.00 s, the mass passes through the equilibrium position (x = 0.00 m) moving to the left. At time t = 0.85 s, the mass reaches the left endpoint (x = - 0.16 m). a) Write an equation to describe the motion of the mass throughout time. [4] b) Find the spring constant, k. [2] c) Find the maximum speed of the mass. [2] d) At what time does the mass first experience the largest possible negative acceleration? [2]

Answer 1

mm x aris N=-0.16 x=0 Displacement for a for a SHM of spring is x (+) - Ao sin (wt+Q) Werd, A Amplitude 0.16 phase dingle. Give at t=0 = 0 xlo) Ao sin (Wxot0) = 0 sind 00=0 al Displacment = x (t) = 0.16 sin wr Giren, half time period I= 0.855 T = 1.75 Angular relocity wa 2 IT T 2T -3.70 radlo 1.7 Equation of motion dx - wx = 0 dt2 an da2 - (308x-of an 3% Spung constant, ſt 12 mw? 3.50x (3.7) 47.9 N/m. may Maximum speed 29 = WA = 3.7 XD-16 = 0. 592 m/s d. Largest posible negative accleration occur when mass is at sight most point. Time 't = 0.85 +2=1.75