11 Problem 4 A mass m1 44 kg is at the end of a horizontal

(11 %) Problem 4: A mass m1 = 4.4 kg is at the end of a horizontal spring of spring constant k = 425 N/m on a frictionless horizontal surface. The block is pulled, stretching the spring a distance A = 45 cm from equilibrium, and released from rest. 17% Part (a) Write an equation for the angular frequency of the oscillation. 17% Part (b) Calculate the angular frequency of the oscillation in rad/seconds. 17% Part (c) Write an equation for the period T of the oscillations. 17% Part (d) Calculate the period T of the oscillations in seconds. 17% Part (e) write an equation for the maximum speed vmax of the block. 17% Part (f) Write an equation for the maximum acceleration antar of the block. Gr De amax

Solution

(A) w = sqrt(k /m )

(b) w = sqrt(425 / 4.4)

w = 9.83 rad/s

(c) T = 2 pi / w = 2 pi sqrt( m / k )

(D) T = 2 pi sqrt(4.4/425) = 0.64 sec  

(e) v_max= A w = A sqrt(k/m)

(f) v_max = 4.5 x sqrt(425/4.4)  

= 44.2 cm/s or 0.442 m/s