F = -82 * .12 = -9.84 N, I can not rad your sign so I will assume -
F = m a = -kx
m a = .82 x
let w = 2 pi f = 2 pi /T
if x = A sin w t
dx/dt = v = A w cos w t
a = dv/dt = -A w^2 sin w t = -w^2 x
so m a = - m w^2 x = - k x
w^2 = k/m
w = 2 pi f = sqrt (k/m)
f = ( 1 / 2pi ) sqrt (82 / 0.75) = 1.67 Hz
max v = A w
max a = A w^2
A block of mass m 0.750 kg is fastened to an unstrained hor- izontal spring whose spring constant is k 82.0 N/m. The block is given a displacement of 0.120 m, where the sign indicates that the dis- placement is along the x axis, and then released from rest. (a) What is the force (magnitude and direction) that the spring exerts on the block just before the block is released? (b) Find the angular frequency of the resulting oscillatory motion. (c) What is the maximum speed of the block? (d) Determine the magnitude of the maximum acceleration of the block.
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