A mass is attached to the end of a spring and set into oscillation on a horizont

Question

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position of x = +0.150 m. The mass of the block is m = 0.647 kg, the force constant of the spring is k = 51.3 N/m.

Determine the following.

(a) force component that the spring exerts on the block just before the block is released (Indicate the direction with the sign of your answer.)
______ N

(b) angular frequency ? of the resulting oscillatory motion
______ rad/s

(c) maximum speed of the oscillating mass
______ m/s

(d) magnitude of the maximum acceleration of the oscillating mass
______ m/s2

Explanation / Answer

(A) F = k x

F = (51.3 N/m) (0.150 m)

F = 7.70 N  

(B) w = sqrt(k/m) = sqrt(51.3/0.647)

w = 8.90 rad/s

(C) A = 0.150 m

v_max = A w = 1.34 m/s

(D) a_max = A w^2 = (0.150)(8.90^2)

a_max = 11.9 m/s^2

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