a )Problem 3 [30 points] An object of mass 2 kg, resting on a frictionless table

Question

a )Problem 3 [30 points] An object of mass 2 kg, resting on a frictionless table, is attached to the wall by a spring. A force of 8 nt is applied to the mass, stretching the spring and moving the mass 0.5 m from its equilibrium position. The object is then released Va) (10 points) Find the resulting motion of the object as a function of time. (b) (10 points] Determine the amplitude. (c) [10 points] At what time does the mass first pass through the equilibrium position? What is its velocity at time?

Explanation / Answer

FORCE = MASS X ACCELERATION FORCE = 8 NT, MASS = 2KG

8 = 2 X a , a= 4 M/S2

(a) NOW INITIAL VELOCITY OF MASS u = 0 , FINAL VELOCITY = v , AND TIME = t

THEN USING FORMULA v= u+ a t , v = 0 + 4 x t v = 4 t REQUIRED MOTION AS FUNCTION OF TIME.

(B) USING S = u t + 1/2 at2  FOR AMPLITUDE S = 0.t + 1/2 x 4 x t2   

S = 2 t2 .....................(1)

(c) TO REACH EQULIBRIUM POSITION S = 0.5 M

PUTTING IN TEQUATION (1) 0.5 = 2 t2   , t2= 0.5/2 = 0.25 hence t = 0.5 sec

VELOCITY AT THIS TIME v = 4 x 0.5 = 2 m/sec

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